Two of the three electrons in a lithium atom have quantum numbers n , l , m f , m s of 1 , 0 , 0 , + 1 2 and 1 , 0 , 0 , - 1 2 . What quantum numbers are possible for the third electron if the atom is ( a ) in the ground state and ( b ) in the first excited state?

The four quantum numbers n , l , m l , m s identify the quantum states of individual electrons in a multi-electron atom. A lithium atom has three electrons. The first two electrons have quantum numbers ( 1 , 0 , 0 , ± 1 / 2 ) . All states with principal quantum number n = 1 are filled. The next lowest states have n = 2 . The orbital quantum number can have the values l = 0 or 1 and of these, the l = 0 states have the lowest energy. The magnetic quantum number must be m l = 0 , since this is the only possibility if l = 0 . The spin quantum number can have either of the values m s = - 1 2 or + 1 2 . Since there is no external magnetic field, the energies of these two states are the same. ( a ) Therefore, in the ground state, the quantum numbers of the third electron are either n = 2 , l = 0 , m l = 0 , m s = - 1 2 or n = 2 , l = 0 , m l = 0 , m s = + 1 2 . That is, n , l , m l , m s = ( 2 , 0 , 0 , + 1 / 2 ) and ( 2 , 0 , 0 , - 1 / 2 ) . ( b ) The next lowest state in energy is an n = 2 , l = 1 state. All n = 3 states are higher in energy. The magnetic quantum number can be m l = - 1 , 0 , or + 1 , the spin quantum number can be m s = - 1 2 or + 1 2 . Thus, n , l , m l , m s = ( 2 , 1 , 1 , + 1 / 2 ) , ( 2 , 1 , 1 , - 1 / 2 ) , ( 2 , 1 , 0 , + 1 / 2 ) , ( 2 , 1 , 0 , - 1 / 2 ) , ( 2 , 1 , - 1 , + 1 / 2 ) and ( 2 , 1 , - 1 , - 1 / 2 ) . No two electrons can have the same set of quantum numbers, as required by the Pauli exclusion principle.

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JEE Main

IMPORTANT

Earn 100

Show that a moving electron cannot spontaneously change into an x-ray photon in free space. A third body (atom or nucleus) must be present. Why is it needed? (Hint: Examine the conservation of energy and momentum.)

Important Questions on All About Atoms

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IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 16

A population inversion for two energy levels is often described by assigning a negative Kelvin temperature to the system. What negative temperature would describe a system in which the population of the upper energy level exceeds that of the lower level by

10 %

and the energy difference between the two levels is

2.32 eV ?

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IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 17

Two of the three electrons in a lithium atom have quantum numbers

(n, l, m_{f}, m_{s})

(1, 0, 0, + \frac{1}{2})

and

(1, 0, 0, - \frac{1}{2}) .

What quantum numbers are possible for the third electron if the atom is

(a)

in the ground state and

(b)

in the first excited state?

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JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 19

A pulsed laser emits light at a wavelength of

694.4 nm .

The pulse duration is

12 ps,

and the energy per pulse is

0.150 J .

(a)

What is the length of the pulse?

(b)

How many photons are emitted in each pulse?

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 20

From Figure

40 - 13,

calculate approximately the energy difference,

E_{L} - E_{M}

, for molybdenum. Compare it with the value that may be obtained from Figure

40 - 15 .

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JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 21

A helium-neon laser emits laser light at a wavelength of

632.8 nm

and a power of

2.3 mW .

At what rate are photons emitted by this device?

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 22

For a helium atom in its ground state, what are quantum numbers

(n, l, m_{l}, m_{s})

for the

(a)

spin-up electron and

(b)

spin-down electron?

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IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 24

15 keV

electron is brought to rest by colliding twice with target nuclei(Assume the nuclei remain stationary.). The wavelength associated with the photon emitted in the second collision is

130 pm

greater than that associated with the photon emitted in the first collision.

(a)

What is the kinetic energy of the electron after the first collision? What are

(b)

the wavelength

λ_{1}

and

(c)

the energy

E_{1}

associated with the first photon? What are

(d)

λ_{2}

and

(e)

E_{2}

associated with the second photon?

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 37 - All About Atoms>Problems>Q 26

A laser emits

424 nm

in a single pulse that lasts

0.500 μs

. The power of the pulse is

3.25 MW .

If we assume that the atoms contributing to the pulse underwent stimulated emission only once during the

0.500 μs,

how many atoms contributed?

Show that a moving electron cannot spontaneously change into an x-ray photon in free space. A third body (atom or nucleus) must be present. Why is it needed? (Hint: Examine the conservation of energy and momentum.)

Important Questions on All About Atoms

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