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Work function of a metal $X$ equals the ionization energy of $L i^{2 +}$ ion in second excited state. Work function of another metal $Y$ equals the ionization energy of $H e^{+}$ ion with electron in $n = 4$ . Now photons of energy $E$ fall separately on both the metals such that maximum kinetic energy of photoelectron emitted from metal $X$ is half that of photoelectron emitted from metal $Y$ . Choose the correct statement ( $E_{0} =$ Potential energy of electron in ground state of hydrogen atom)

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Important Questions on Atoms and Nuclei

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

The amount of energy required to separate a hydrogen atom into a proton and an electron is

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

A hydrogen atom is in the ground state. Then to get six lines in an emission spectrum, wavelength of the incident radiation should be

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

In the hydrogen atom spectrum, let

E_{1}

and

E_{2}

are energies for the transition

n = 2 \to n = 1

and

n = 3 \to n = 2

respectively. The ratio

E_{2} / E_{1}

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

Energy of an electron in the lowest energy state of the hydrogen atom

= 13.6 eV

. Find the energy needed to remove an electron from the fourth orbit.

HARD

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which perfactly inelastic collision will take place is :

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

The ionization potential of hydrogenic ions

P

and

Q

are

V_{P}

and

V_{Q}

respectively. If

V_{Q} < V_{P}

then radii

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

Minimum excitation potential of Bohr's first orbit of Hydrogen atom is_____.

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

A hydrogen atom in the ground state absorbs,

∆ E

amount of energy. If the orbital angular momentum of the electron is increased by

\frac{h}{2 π}

(

h =

Plank constant), then the magnitude of

Δ E

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

H e^{+}

ion is in its first excited state. Its ionization energy is:

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

Monochromatic radiation of wavelength

λ

is incident on a hydrogen sample in ground state. Hydrogen atom absorbs a fraction of light and subsequently emits radiations of six different wavelengths. The wavelength

λ

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

λ_{2}

and

λ_{4}

are the wavelengths of photons required to excite the Hydrogen atom from its ground state to its second and fourth excited states, respectively. What is the correct ratio

λ_{2} / λ_{4}

HARD

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

Consider a hydrogen-like ionized atom with atomic number

Z

with a single electron. In the emission spectrum of this atom, the photon emitted in the

n = 2 t o n = 1

transition has energy

74.8 eV

higher than the photon emitted in the

n = 3 t o n = 2

transition. Given that the ionization energy of the hydrogen atom is

13.6 eV

, what is the value of

Z

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

The ionization potential of hydrogen atom is

13.6 V

. How much energy need to be supplied to ionize the hydrogen atom in the first excited state.

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

Imagine that the electron in a hydrogen atom is replaced by a muon

(μ) .

The mass of muon particle is

207

times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:-

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

A hydrogen atom is in an excited state of principal quantum number

(n) .

It emits a photon of wavelength

λ

when it returns to the ground state, the value of

' n'

is ________

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

Calculate the longest and shortest wavelength in the Lyman series of hydrogen emission spectrum. ( Rydberg constant

R = 1.1 \times 10^{7} m^{- 1}

)

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

If the light from Balmer series of hydrogen is used to eject photoelectrons from a metal, then the maximum work function of the metal can be

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

12 eV

energy is given to electron in third orbit of

H

-atom, then final energy of electron when it ionise from third orbit, is

HARD

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

A singly ionized helium atom in an excited state

(n = 4)

emits a photon of energy

2.6 eV

. Given that the ground state energy of hydrogen atom is

13.6 eV

, the energy

(E_{t})

and quantum number

(n)

of the resulting state are respectively,

EASY

Physics>Modern Physics>Atoms and Nuclei>Bohr’s Theory of Hydrogen-Like Atoms

The energy required to remove the electron from a singly ionized Helium atom is

2.2

times the energy required to remove an electron from helium atom. The total energy required to ionize the Helium atom completely is close to

Important Questions on Atoms and Nuclei

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