Which of the following statement(s) is (are) correct about the spectrum of hydrogen atom?

The wavelength ranges of Lyman and Balmer series do not overlap.

There is an overlap between the wavelength ranges of Balmer and Paschen series.

The wavelengths of Lyman series are given by 1 + 1 m 2 λ 0 , where λ 0 is the shortest wavelength of Lyman series and m is an integer.

A particle of mass m moves in circular orbits with potential energy U r = F r , where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by R and its speed and energy are denoted by v and E respectively, then for the n th orbit (here h is the Planck's constant)

E = 3 2 n 2 h 2 F 2 4 π 2 m 1 / 3

R ∝ n 1 / 3 and v ∝ n 2 / 3

E = 2 n 2 h 2 F 2 4 π 2 m 1 / 3

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Highly excited states for hydrogen like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >> 1. Which of the following statement(s) is (are) true?

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Important Questions on Atoms and Nuclei

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2021>Q 1

A heavy nucleus

N

, at rest, undergoes fission

N \to P + Q,

where

P

and

Q

are two lighter nuclei. Let

δ = M_{N} - M_{P} - M_{Q}

, where

M_{P}, M_{Q}

and

M_{N}

are the masses of

P, Q

and

N

, respectively.

E_{P}

and

E_{Q}

are the kinetic energies of

P

and

Q

, respectively. The speeds of

P

and

Q

are

v_{P}

and

v_{Q}

, respectively. If

c

is the speed of light, which of the following statement(s) is (are) correct?

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2020>Q 2

In an

X

-ray tube, electrons emitted from a filament (cathode) carrying current

I

hit a target (anode) at a distance

d

from the cathode. The target is kept at a potential

V

higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current

I

is decreased to

\frac{I}{2},

the potential difference

V

is increased to

2 V,

and the separation distance

d

is reduced to

\frac{d}{2},

then

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2019>Q 3

A free hydrogen atom after absorbing a photon of wavelength

λ_{a}

gets excited from the state

n = 1

to the state

n = 4 .

Immediately after that the electron jumps to

n = m

state by emitting a photon of wavelength

λ_{e} .

Let the change in momentum of atom due to the absorption and the emission are

Δ p_{a}

and

Δ p_{e},

respectively. If

\frac{λ_{a}}{λ_{e}} = \frac{1}{5},

which of the option(s) is/are correct?
[Use

h c = 1242 e V n m, 1 n m = 10^{- 9} m,

h

and

c

are Planck's constant and speed of light, respectively]

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2019>Q 4

Suppose a

{}_{88}^{226}{R a}

nucleus at rest and in ground state undergoes

α

-decay to a

{}_{86}^{222}{R n}

nucleus in its excited state. The kinetic energy of the emitted

α

particle is found to be

4.44 M e V . {}_{86}^{222}R n

nucleus then goes to its ground state by

γ

-decay. The energy of the emitted

γ

-photon is _______

k e V,

[Given: atomic mass of

_{88}^{226} R a = 226.005 u,

atomic mass of

_{86}^{222} R n = 222.000 u,

atomic mass of

α

particle

= 4.000 u, 1 u = 931 M e V / c^{2}, c

is speed of the light]

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2018>Q 5

In a radioactive decay chain,

_{90}^{232} Th

nucleus decays to

_{82}^{212} Pb

nucleus. Let

N_{α} and N_{β}

be the number of

α and β^{-}

particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2018>Q 6

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

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2016>Q 7

The electrostatic energy of

Z

protons uniformly distributed throughout a spherical nucleus of radius

R

is given by,

E = \frac{3}{5} \frac{Z (Z - 1) e^{2}}{4 π ε_{0} R}

. The measured masses of the neutron,

{}_{1}^{1}H, {}_{7}^{15}N and {}_{8}^{15}O

are

1.008665 u

1.007825 u, 15.000109 u and 15.003065 u

respectively. Given that the radii of both the

{}_{7}^{15}N and {}_{8}^{15}O

nuclei are same,

1 u = 931.5 MeV c^{- 2}

(

c

is the speed of light) and

\frac{e^{2}}{(4 π ϵ_{0})} = 1.44 MeV fm

. Assuming that the difference between the binding energies of

{}_{7}^{15}N a n d {}_{8}^{15}O

is purely due to the electrostatic energy, the radius of either of the nuclei is

(1 fm = 10^{- 15} m)

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 21 - Atoms and Nuclei>JEE Advanced Paper 2 - 2016>Q 8

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life

18

days inside the laboratory. Tests revealed that the radiation was

64

times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

Highly excited states for hydrogen like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >> 1. Which of the following statement(s) is (are) true?

Important Questions on Atoms and Nuclei

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