## Following results are observed when sodium metal is irradiated with different wavelengths.

[question] Question. Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and, (b) Planck’s constant [/question] [solution] Solution: (a) Assuming the threshold wavelength to be $\lambda_{0} \mathrm{~nm}\left(=\lambda_{0} \times 10^{-9} \mathrm{~m}\right)$, the kinetic energy of the radiation is given as: $\mathrm{h}\left(v-v_{0}\right)=\frac{1}{2} m v^{2}$ Three different equalities can be formed by the given value as: $h ...

## The work function for caesium atom is 1.9 eV. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation

[question] Question. The work function for caesium atom is $1.9 \mathrm{eV}$. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength $500 \mathrm{~nm}$, calculate the kinetic energy and the velocity of the ejected photoelectron. [/question] [solution] Solution: It is given that the work function $\left(W_{0}\right)$ for caesium atom is $1.9 \mathrm{eV}$. (a) From the $W_{0}=\frac{h c}{\lambda_{0}}$ expressio...

## Lifetimes of the molecules in the excited states are often measured

[question] Question. Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nano second range. If the radiation source has the duration of $2 \mathrm{~ns}$ and the number of photons emitted during the pulse source is $2.5 \times$ $10^{15}$, calculate the energy of the source. [/question] [solution] Solution: Frequency of radiation (v), $v=\frac{1}{2.0 \times 10^{-9} \mathrm{~s}}$ $v=5.0 \times 10^{8} \mathrm{~s}^{-1}$ Energy...

## Lifetimes of the molecules in the excited states are often measured

[question] Question. Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nano second range. If the radiation source has the duration of $2 \mathrm{~ns}$ and the number of photons emitted during the pulse source is $2.5 \times$ $10^{15}$, calculate the energy of the source. [/question] [solution] Solution: Frequency of radiation $(v)$, $v=\frac{1}{2.0 \times 10^{-9} \mathrm{~s}}$ $v=5.0 \times 10^{8} \mathrm{~s}^{-1}$ Ener...

## In astronomical observations, signals observed from the distant stars are generally weak.

[question] Question. In astronomical observations, signals observed from the distant stars are generally weak. If the photon detector receives a total of $3.15 \times 10^{-18} \mathrm{~J}$ from the radiations of $600 \mathrm{~nm}$, calculate the number of photons received by the detector. [/question] [solution] Solution: From the expression of energy of one photon $(E)$, $E=\frac{\text { he }}{\lambda}$ Where, $\lambda=$ wavelength of radiation $h=$ Planck's constant $c=$ velocity of radiation S...

## Neon gas is generally used in the sign boards.

[question] Question. Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate (a) the frequency of emission, (b) distance traveled by this radiation in 30 s (c) energy of quantum and (d) number of quanta present if it produces 2 J of energy. [/question] [solution] Solution: Wavelength of radiation emitted $=616 \mathrm{~nm}=616 \times 10^{-9} \mathrm{~m}$ (Given) (a) Frequency of emission $(v)$ $v=\frac{c}{\lambda}$ Where, $c=$ velocity of radiation $\lambda=$ wav...

## Nitrogen laser produces a radiation at a wavelength of 337.1 nm.

[question] Question. Nitrogen laser produces a radiation at a wavelength of $337.1 \mathrm{~nm}$. If the number of photons emitted is $5.6 \times 10^{24}$, calculate the power of this laser. [/question] [solution] Solution: Power of laser = Energy with which it emits photons Power $=E=\frac{\text { Nhe }}{\lambda}$ Where, N = number of photons emitted h = Planck’s constant c = velocity of radiation $\lambda=$ wavelength of radiation Substituting the values in the given expression of Energy (E): ...

## Arrange the following type of radiations in increasing order of frequency:

[question] Question. Arrange the following type of radiations in increasing order of frequency: (a) radiation from microwave oven (b) amber light from traffic signal (c) radiation from FM radio (d) cosmic rays from outer space and (e) X-rays [/question] [solution] Solution: The increasing order of frequency is as follows: Radiation from FM radio < amber light < radiation from microwave oven < X- rays < cosmic rays The increasing order of wavelength is as follows: Cosmic rays < X-rays < radiation...

## An ion with mass number 56 contains 3 units of positive charge

[question] Question. An ion with mass number 56 contains 3 units of positive charge and 30.4% more neutrons than electrons. Assign the symbol to this ion. [/question] [solution] Solution: Let the number of electrons present in ion $\mathrm{A}^{3+}$ be $x$. $\therefore$ Number of neutrons in it $=x+30.4 \%$ of $x=1.304 x$ Since the ion is tripositive, $\Rightarrow$ Number of electrons in neutral atom $=x+3$ $\therefore$ Number of protons in neutral atom $=x+3$ Given, Mass number of the ion $=56$ ...

## An ion with mass number 37 possesses one unit of negative charge.

[question] Question. An ion with mass number 37 possesses one unit of negative charge. If the ion contains 11.1% more neutrons than the electrons, find the symbol of the ion. [/question] [solution] Solution: Let the number of electrons in the ion carrying a negative charge be x. Then, Number of neutrons present $=x+11.1 \%$ of $x$ $=x+0.111 x$ $=1.111 x$ Number of electrons in the neutral atom $=(x-1)$ (When an ion carries a negative charge, it carries an extra electron) $\therefore$ Number of p...

## An element with mass number 81 contains 31.7% more neutrons as compared to protons.

[question] Question. An element with mass number 81 contains 31.7% more neutrons as compared to protons. Assign the atomic symbol. [/question] [solution] Solution: Let the number of protons in the element be $x$. Number of neutrons in the element $=x+31.7 \%$ of $x$ $=x+0.317 x$ $=1.317 x$ According to the question, Mass number of the element = 81 $\therefore$ (Number of protons $+$ number of neutrons $)=81$ $\Rightarrow x+1.317 x=81$ $2.317 x=81$ $x=\frac{81}{2.317}$ $=34.95$ $\therefore x=35$ ...

## Symbols ${ }_{35}^{79} \mathrm{Br}$ and ${ }^{79} \mathrm{Br}$ can be written

[question] Question. Symbols ${ }_{35}^{79} \mathrm{Br}$ and ${ }^{79} \mathrm{Br}$ can be written, whereas symbols ${ }_{79}^{35} \mathrm{Br}$ and ${ }^{35} \mathrm{Br}$ are not acceptable. Answer briefly. [/question] [solution] Solution: The general convention of representing an element along with its atomic mass $(A)$ and atomic number $(Z)$ is ${ }_{Z}^{A} \mathrm{X}$. Hence, ${ }_{15}^{79} \mathrm{Br}$ is acceptable but is ${ }_{79}^{35} \ mathrm {Br}$ not acceptable. ${ }^{79} \mathrm{Br}$...

## In Rutherford’s experiment, generally the thin foil of heavy atoms, like gold, platinum etc.

[question] Question. In Rutherford’s experiment, generally the thin foil of heavy atoms, like gold, platinum etc. have been used to be bombarded by the α-particles. If the thin foil of light atoms like Aluminium etc. is used, what difference would be observed from the above results? [/question] [solution] Solution: A thin foil of lighter atoms will not give the same results as given with the foil of heavier atoms. Lighter atoms would be able to carry very little positive charge. Hence, they will...

## In Milikan’s experiment,

[question] Question. In Milikan's experiment, static electric charge on the oil drops has been obtained by shining X-rays. If the static electric charge on the oil drop is $-1.282 \times 10^{-18} \mathrm{C}$, calculate the number of electrons present on it. [/question] [solution] Solution: Charge on the oil drop $=1.282 \times 10^{-18} \mathrm{C}$ Charge on one electron $=1.6022 \times 10^{-19} \mathrm{C}$ Number of electrons present on the oil drop $=\frac{1.282 \times 10^{-18} \mathrm{C}}{1.60...

## A certain particle carries $2.5 \times 10^{-16} \mathrm{C}$ of static electric charge.

[question] Question. A certain particle carries $2.5 \times 10^{-16} \mathrm{C}$ of static electric charge. Calculate the number of electrons present in it. [/question] [solution] Solution: Charge on one electron $=1.6022 \times 10^{-19} \mathrm{C}$ $\Rightarrow 1.6022 \times 10^{-19} \mathrm{C}$ charge is carried by 1 electron. $\therefore$ Number of electrons carrying a charge of $2.5 \times 10^{-16} \mathrm{C}$ $=\frac{1}{1.6022 \times 10^{-19} \mathrm{C}}\left(2.5 \times 10^{-16} \mathrm{C}\...

## The diameter of zinc atom is $2.6 \mathrm{~A}$. Calculate

[question] Question. The diameter of zinc atom is $2.6 \mathrm{~A}$. Calculate (a) radius of zinc atom in $\mathrm{pm}$ and (b) number of atoms present in a length of $1.6 \mathrm{~cm}$ if the zinc atoms are arranged side by side lengthwise. [/question] [solution] Solution: (a) Radius of zinc atom $=\frac{\text { Diameter }}{2}$ $=\frac{2.6 \mathrm{~A}}{2}$ $=1.3 \times 10^{-10} \mathrm{~m}$ $=130 \times 10^{-12} \mathrm{~m}=130 \mathrm{pm}$ (b) Length of the arrangement $=1.6 \mathrm{~cm}$ $=1....

## $2 \times 10^{8}$ atoms of carbon are arranged side by side.

[question] Question. $2 \times 10^{8}$ atoms of carbon are arranged side by side. Calculate the radius of carbon atom if the length of this arrangement is $2.4 \mathrm{~cm}$. [/question] [solution] Solution: Length of the given arrangement = 2.4 cm Number of carbon atoms present $=2 \times 10^{8}$ Diameter of carbon atom $=\frac{2.4 \times 10^{-2} \mathrm{~m}}{2 \times 10^{8}}$ $=1.2 \times 10^{-10} \mathrm{~m}$ $\therefore$ Radius of carbon atom $=\frac{\text { Diameter }}{2}$ $=\frac{1.2 \time...

## If the diameter of a carbon atom is 0.15 nm,

[question] Question. If the diameter of a carbon atom is 0.15 nm, calculate the number of carbon atoms which can be placed side by side in a straight line across length of scale of length 20 cm long. [/question] [solution] Solution: $1 \mathrm{~m}=100 \mathrm{~cm}$ $1 \mathrm{~cm}=10^{-2} \mathrm{~m}$ Length of the scale $=20 \mathrm{~cm}$ $=20 \times 10^{-2} \mathrm{~m}$ Diameter of a carbon atom $=0.15 \mathrm{~nm}$ $=0.15 \times 10^{-9} \mathrm{~m}$ One carbon atom occupies $0.15 \times 10^{-...

## Calculate the energy required for the process

[question] Question. Calculate the energy required for the process $\mathrm{He}_{(\mathrm{g})}^{+} \rightarrow \mathrm{He}^{2+}{ }_{(\mathrm{g})}+\mathrm{e}^{-}$ The ionization energy for the $\mathrm{H}$ atom in the ground state is $2.18 \times 10^{-18} \mathrm{~J}$ atom $^{-1}$ [/question] [solution] Solution: Energy associated with hydrogen-like species is given by, $E_{n}=-2.18 \times 10^{-18}\left(\frac{Z^{2}}{n^{2}}\right) \mathrm{J}$ For ground state of hydrogen atom, $\Delta E=E_{\infty}...

## What transition in the hydrogen spectrum would have

[question] Question. What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition $n=4$ to $n=2$ of $\mathrm{He}^{+}$spectrum? [/question] [solution] Solution: For $\mathrm{He}^{+}$ion, the wave number $(\bar{v})$ associated with the Balmer transition, $n=4$ to $n$ $=2$ is given by: $\bar{v}=\frac{1}{\lambda}=R Z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$ Where, $n_{1}=2$ $n_{2}=4$ $Z=$ atomic number of helium $\bar{v}=\frac{1}{\lambda}=R(2)^{2}\...

## Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple

[question] Question. Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit. [/question] [solution] Solution: Since a hydrogen atom has only one electron, according to Bohr’s postulate, the angular momentum of that electron is given by: $m v r=n \frac{\mathrm{h}}{2 \pi} \ldots \ldots \ldots(1)$ Where, $n=1,2,3, \ldots$ According to de Broglie’s equation: $\lambda=\frac{\mathr...

## How many electrons in an atom may have the following quantum numbers?

[question] Question. How many electrons in an atom may have the following quantum numbers? (a) $n=4$ $m_{x}=-\frac{1}{2}$ (b) $n=3, I=0$ [/question] [solution] Solution: (a) Total number of electrons in an atom for a value of $n=2 n^{2}$ $\therefore$ For $n=4$, Total number of electrons $=2(4)^{2}=32$ The given element has a fully filled orbital as $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10}$ Hence, all the electrons are paired. $\therefore$ Number of electrons (having $n=4$ and $\...

## Explain, giving reasons, which of the following sets of quantum numbers are not possible.

[question] Question. Explain, giving reasons, which of the following sets of quantum numbers are not possible. (a) $n=0 I=0 m_{\imath}=0$ $m_{s}=+\frac{1}{2}$ (b) $n=1 I=0 m_{\imath}=0$ $m_{x}=-\frac{1}{2}$ (c) $n=1 I=1 m_{l}=0$ $m_{x}=+\frac{1}{2}$ (d) $n=2 l=1 m i=0$ $m_{x}=+\frac{1}{2}$ (e) $n=3 I=3 m_{l}=-3$ $m_{x}=+\frac{1}{2}$ (f) $n=3 I=1 m_{l}=0$ $m_{x}=+\frac{1}{2}$ [/question] [solution] Solution: (a) The given set of quantum numbers is not possible because the value of the principal q...

## Using $s, p, d$ notations, describe the orbital with the following quantum numbers.

[question] Question. Using s, p, d notations, describe the orbital with the following quantum numbers. (a) $n=1, I=0 ;$ (b) $n=3 ; I=1$ (c) $n=4 ; I=2 ;$ (d) $n=4 ; I=3$ [/question] [solution] Solution: (a) $n=1, I=0$ (Given) The orbital is $1 s$. (b) For $n=3$ and $I=1$ The orbital is $3 p$. (c) For $n=4$ and $I=2$ The orbital is $4 d$. (d) For $n=4$ and $I=3$ The orbital is $4 f$. [/solution]...

## An atomic orbital has $n=3$. What are the possible values of $/$ and $m_{l}$ ?

[question] Question. (i) An atomic orbital has $n=3$. What are the possible values of $/$ and $m_{l}$ ? (ii) List the quantum numbers ( $m$ i and $I$ ) of electrons for $3 d$ orbital. (iii) Which of the following orbitals are possible? $1 p, 2 s, 2 p$ and $3 f$ [/question] [solution] Solution: (i) $n=3$ (Given) For a given value of $n, I$ can have values from 0 to $(n-1)$. $\therefore$ For $n=3$ $I=0,1,2$ For a given value of $I, m_{1}$ can have $(2 I+1)$ values. For $I=0, m=0 I=1, m=-1,0,1 I=2,...

## Give the number of electrons in the species

[question] Question. Give the number of electrons in the species $\mathrm{H}_{2}^{+}, \mathrm{H}_{2}$ and $\mathrm{O}_{2}^{+}$ [/question] [solution] Solution: $\mathrm{H}_{2}^{+}$: Number of electrons present in hydrogen molecule (H2) = 1 + 1 = 2 $\therefore$ Number of electrons in $\mathrm{H}_{2}^{+}=2-1=1$ H2: Number of electrons in H2 = 1 + 1 = 2 $\mathrm{O}_{2}^{+}$ Number of electrons present in oxygen molecule $\left(\mathrm{O}_{2}\right)=8+8=16$ $\therefore$ Number of electrons in $\math...

## An atom of an element contains 29 electrons and 35 neutrons. Deduce

[question] Question. An atom of an element contains 29 electrons and 35 neutrons. Deduce (i) the number of protons and (ii) the electronic configuration of the element. [/question] [solution] Solution: (i) For an atom to be neutral, the number of protons is equal to the number of electrons. Number of protons in the atom of the given element = 29 (ii) The electronic configuration of the atom is $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10}$ [/solution]...

## An electron is in one of the 3d orbitals

[question] Question. An electron is in one of the $3 d$ orbitals. Give the possible values of $n, I$ and $m_{1}$ for this electron. [/question] [solution] Solution: For the $3 d$ orbital: Principal quantum number $(n)=3$ Azimuthal quantum number $(I)=2$ Magnetic quantum number $\left(m_{i}\right)=-2,-1,0,1,2$ [/question]...

## What is the lowest value of n that allows g orbitals to exist?

[question] Question. What is the lowest value of n that allows g orbitals to exist? [/question] [solution] Solution: For $\mathrm{q}$-orbitals, $I=4$. As for any value ' $n$ ' of principal quantum number, the Azimuthal quantum number $(I)$ can have a value from zero to $(n-1)$. $\therefore$ For $I=4$, minimum value of $n=5$ [/solution]...

## Write the electronic configurations of the following ions:

[question] Question. (i) Write the electronic configurations of the following ions: (a) $\mathrm{H}^{-}$ (b) $\mathrm{Na}^{+}$ (c) $\mathrm{O}^{2-}$ (d) $\mathrm{F}^{-}$ (ii) What are the atomic numbers of elements whose outermost electrons are represented by (a) $3 s^{1}$ (b) $2 p^{3}$ and (c) $3 p^{5} ?$ (iii) Which atoms are indicated by the following configurations? (a) $[\mathrm{He}] 2 s^{1}$ (b) [Ne] $3 s^{2} 3 p^{3}$ (c) $[\mathrm{Ar}] 4 s^{2} 3 d^{1}$. [/question] [solution] Solution: (i...

## The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$.

[question] Question. The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$. If its K.E. is $3.0 \times 10^{-25} \mathrm{~J}$, calculate its wavelength. [/question] [solution] Solution: From de Broglie’s equation, $\lambda=\frac{\mathrm{h}}{m \mathrm{v}}$ Given, Kinetic energy (K.E) of the electron $=3.0 \times 10^{-25} \mathrm{~J}$ Since $\mathrm{K} . \mathrm{E}=\frac{1}{2} m v^{2}$ $\therefore$ Velocity $(v)=\sqrt{\frac{2 K \cdot E}{m}}$ $=\sqrt{\frac{2\left(3.0 \times 10^{-25} \mathrm{...

## The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$. If its K.E. is $3.0 \times 10^{-25} \mathrm{~J}$,

[question] Question. The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$. If its K.E. is $3.0 \times 10^{-25} \mathrm{~J}$, calculate its wavelength. [/question] [solution] Solution: From de Broglie’s equation, $\lambda=\frac{\mathrm{h}}{m v}$ Given, Kinetic energy (K.E) of the electron $=3.0 \times 10^{-25} \mathrm{~J}$ Since $\mathrm{K} . \mathrm{E}=\frac{1}{2} m v^{2}$ $\therefore$ Velocity $(v)=\sqrt{\frac{2 \mathrm{~K} \cdot \mathrm{E}}{m}}$ $=\sqrt{\frac{2\left(3.0 \times 10^{-25...

## The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$.

[question] Question. The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$. If its K.E. is $3.0 \times 10^{-25} \mathrm{~J}$, calculate its wavelength. [/question] [solution] Solution: From de Broglie’s equation, $\lambda=\frac{\mathrm{h}}{m v}$ Given, Kinetic energy (K.E) of the electron $=3.0 \times 10^{-25} \mathrm{~J}$ Since $\mathrm{K} . \mathrm{E}=\frac{1}{2} m v^{2}$ $\therefore$ Velocity $(v)=\sqrt{\frac{2 \mathrm{~K} \cdot \mathrm{E}}{m}}$ $=\sqrt{\frac{2\left(3.0 \times 10^{-25...

## Calculate the wavelength of an electron moving

[question] Question. Calculate the wavelength of an electron moving with a velocity of $2.05 \times 10^{7} \mathrm{~ms}^{-1}$. [/question] [solution] Solution: According to de Broglie’s equation $\lambda=\frac{\mathrm{h}}{m v}$ Where, $\lambda=$ wavelength of moving particle $m=$ mass of particle $v=$ velocity of particle $\mathrm{h}=$ Planck's constant Substituting the values in the expression of $\lambda$ : $\lambda=\frac{6.626 \times 10^{-34} \mathrm{Js}}{\left(9.10939 \times 10^{-31} \mathrm...

## The electron energy in hydrogen atom is given by

[question] Question. The electron energy in hydrogen atom is given by $E_{n}=\left(-2.18 \times 10^{-18}\right) / n^{2} \mathrm{~J}$. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition? [/question] [solution] Solution: Given $E_{n}=-\frac{2.18 \times 10^{-18}}{n^{2}} \mathrm{~J}$ Energy required for ionization from n = 2 is given by, $\Delta E=E_{\infty}-E_{2}$ $=\left[\left(...

## What is the energy in joules, required to shift the electron of the hydrogen atom

[question] Question. What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is $-2.18 \times 10^{-11}$ ergs. [/question] [solution] Solution: Energy $(E)$ of the $\mathrm{n}^{\text {th }}$ Bohr orbit of an atom is given by, $E_{n}=\frac{-\left(2.18 \times 10^{-18}\right) \mathrm{Z}^{2}}{n^{2}}$...

## Calculate the wave number for the longest wavelength transition

[question] Question. Calculate the wave number for the longest wavelength transition in the Balmer series of atomic hydrogen. [/question] [solution] Solution: For the Balmer series, $n_{i}=2$. Thus, the expression of wavenumber $(\bar{v})$ is given by, $\bar{v}=\left[\frac{1}{(2)^{2}}-\frac{1}{n_{\mathrm{f}}^{2}}\right]\left(1.097 \times 10^{7} \mathrm{~m}^{-1}\right)$ Wave number $(\bar{v})$ is inversely proportional to wavelength of transition. Hence, for the longest wavelength transition, $(\...

## The energy associated with the first orbit in the hydrogen atom

[question] Question. (i) The energy associated with the first orbit in the hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$ atom $^{-1}$. What is the energy associated with the fifth orbit? (ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom. [/question] [solution] Solution: (i)Energy associated with the fifth orbit of hydrogen atom is calculated as: $E_{5}=\frac{-\left(2.18 \times 10^{-18}\right)}{(5)^{2}}=\frac{-2.18 \times 10^{-18}}{25}$ $E_{5}=-8.72 \times 10^{-20} \mathrm{...

## What is the maximum number of emission lines when the excited electron of an H

[question] Question. What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state? [/question] [solution] Solution: When the excited electron of an H atom in n = 6 drops to the ground state, the following transitions are possible: Hence, a total number of (5 + 4 + 3 + 2 + 1) 15 lines will be obtained in the emission spectrum. The number of spectral lines produced when an electron in the $n^{\text {th }}$ level drops down to the ground sta...

## How much energy is required to ionise a H atom if the electron occupies n = 5 orbit?

[question] Question. How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom (energy required to remove the electron from n =1 orbit). [/question] [solution] Solution: The expression of energy is given by, $E_{n}=\frac{-\left(2.18 \times 10^{-18}\right) Z^{2}}{n^{2}}$ Where, Z = atomic number of the atom n = principal quantum number For ionization from $n_{1}=5$ to $n_{2}=\infty$, $\Delta E=E_{x}-E_{3}$ $=\le...

## What is the wavelength of light emitted

[question] Question. What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2? [/question] [solution] Solution: The ni = 4 to nf = 2 transition will give rise to a spectral line of the Balmer series. The energy involved in the transition is given by the relation, $E=2.18 \times 10^{-18}\left[\frac{1}{n_{i}^{2}}-\frac{1}{n_{j}^{2}}\right]$ Substituting the values in the given expression of E $E=...

## Electrons are emitted with zero velocity from a metal surface

[question] Question. Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength 6800 Å. Calculate threshold frequency $\left(\begin{array}{ll}v_{0} & )\end{array}\right.$ and work function (W0) of the metal. [/question] [solution] Solution: Threshold wavelength of radiation $\left(\lambda_{0}\right)=6800 =6800 \times 10^{-10} \mathrm{~m}$ Threshold frequency $\left(v_{0}\right)$ of the metal $=\frac{c}{\lambda_{0}}=\frac{3 \times 10^{8} \mathrm{~m...

## A 25 watt bulb emits monochromatic yellow light of wavelength of 0.57μm.

[question] Question. A 25 watt bulb emits monochromatic yellow light of wavelength of 0.57μm. Calculate the rate of emission of quanta per second [/question] [solution] Solution: Power of bulb, $P=25 \mathrm{Watt}=25 \mathrm{~J} \mathrm{~s}^{-1}$ Energy of one photon, $E=h v=\frac{h c}{\lambda}$ Substituting the values in the given expression of $E$ : $E=\frac{\left(6.626 \times 10^{-34}\right)\left(3 \times 10^{8}\right)}{\left(0.57 \times 10^{-6}\right)}=34.87 \times 10^{-20} \mathrm{~J}$ $\le...

## Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom.

[question] Question. Electromagnetic radiation of wavelength $242 \mathrm{~nm}$ is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in $\mathrm{kJ} \mathrm{mol}^{-1}$. [/question] [solution] Solution: Energy of sodium $(E)=\frac{N_{\Lambda} h c}{\lambda}$ $=\frac{\left(6.023 \times 10^{23} \mathrm{~mol}^{-1}\right)\left(6.626 \times 10^{-34} \mathrm{Js}\right)\left(3 \times 10^{8} \mathrm{~ms}^{-1}\right)}{242 \times 10^{-9} \mathrm{~m}}$ $=4.947 \times 10^{5}...

## A photon of wavelength $4 \times 10^{-7} \mathrm{~m}$ strikes on metal surface,

[question] Question. A photon of wavelength $4 \times 10^{-7} \mathrm{~m}$ strikes on metal surface, the work function of the metal being $2.13 \mathrm{eV}$. Calculate (i) the energy of the photon (ev), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron $\left(1 \mathrm{eV}=1.6020 \times 10^{-19} \mathrm{~J}\right)$. [/question] [solution] Solution: (i) Energy (E) of a photon $=h v=\frac{h c}{\lambda}$ Where, $\mathrm{h}=$ Planck's constant $=6.626 \times 10^{-3...

## What is the number of photons of light with a wavelength

[question] Question. What is the number of photons of light with a wavelength of 4000 pm that provide 1 J of energy? [/question] [solution] Solution: Energy $(E)$ of a photon $=h v$ Energy $\left(E_{n}\right)$ of ' $n$ ' photons $=n h v$ $\Rightarrow n=\frac{E_{n} \lambda}{\text { hc }}$ Where, $\lambda=$ wavelength of light $=4000 \mathrm{pm}=4000$ $\times 10^{-12} \mathrm{~m} \mathrm{c}=$ velocity of light in vacuum $=3 \times 10^{8}$ $\mathrm{m} / \mathrm{s} \mathrm{h}=$ Planck's constant $=6...

## Calculate the wavelength,

[question] Question. Calculate the wavelength, frequency and wave number of a light wave whose period is $2.0 \times 10^{-10} \mathrm{~s} .$ [/question] [solution] Solution: Frequency $(v)$ of light $=\frac{1}{\text { Period }}$ $=\frac{1}{2.0 \times 10^{-10} \mathrm{~s}}=5.0 \times 10^{9} \mathrm{~s}^{-1}$ Wavelength $(\lambda)$ of light $=\frac{c}{v}$ Where $c=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ Substituting the value in the given expression of $\lambda$ :...

## Find energy of each of the photons which

[question] Question. Find energy of each of the photons which (i)correspond to light of frequency 3× 1015 Hz. (ii)have wavelength of 0.50 Å. [/question [solution] Solution: (i) Energy $(E)$ of a photon is given by the expression, $E=h v$ Where, $h=$ Planck's constant $=6.626 \times 10^{-34} \mathrm{Js}$ $v=$ frequency of light $=3 \times 10^{15} \mathrm{~Hz}$ Substituting the values in the given expression of $E$ : $E=\left(6.626 \times 10^{-34}\right)\left(3 \times 10^{15}\right)$ $E=1.988 \tim...

## Yellow light emitted from a sodium lamp has a wavelength

[question] Question. Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wave number $(\bar{v})$ of the yellow light [/question] [solution] Solution: From the expression $\lambda=\frac{\mathrm{c}}{v}$ We get $v=\frac{c}{\lambda}$..........(i) Where, ν= frequency of yellow light $\mathrm{c}=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ $\lambda=$ wavelength of yellow light $=580 \mathrm{~nm}=580 \times 10^{-9} \mathrm...

## Write the complete symbol for the atom with thegiven atomic numbe

[question] Question. Write the complete symbol for the atom with thegiven atomic number (Z) and Atomic mass (A (i)Z = 17, A = 35 (ii)Z = 92, A = 233 (iii)Z = 4, A = 9 [/question] [solution] Solution: (i) ${ }_{17}^{35} \mathrm{Cl}$ (ii) ${ }_{92}^{233} \mathrm{U}$ (iii) ${ }_{4}^{9} \mathrm{Be}$ [/solution]...

## Calculate the total number of electrons present in one mole of methane

[question] Question. (i)Calculate the total number of electrons present in one mole of methane (ii) Find (a) the total number and (b) the total mass of neutrons in $7 \mathrm{mg}$ of ${ }^{14} \mathrm{C}$. (Assume that mass of a neutron $=1.675 \times 10^{-27} \mathrm{~kg}$ ). (iii) Find (a) the total number and (b) the total mass of protons in $34 \mathrm{mg}$ of $\mathrm{NH}_{3}$ at STP. Will the answer change if the temperature and pressure are changed? [/question] [solution] Solution: (i) Nu...

## Calculate the number of electrons which will together weigh one gram

[question] Question. (i)Calculate the number of electrons which will together weigh one gram. (ii)Calculate the mass and charge of one mole of electrons [/question] [solution] Solution: (i) Mass of one electron $=9.10939 \times 10^{-31} \mathrm{~kg}$ $\therefore$ Number of electrons that weigh $9.10939 \times 10^{-31} \mathrm{~kg}=1$ $\therefore$ Number of electrons that will weigh $1 \mathrm{~g}\left(1 \times 10^{-3} \mathrm{~kg}\right)$ $=\frac{1}{9.10939 \times 10^{-31} \mathrm{~kg}} \times\l...