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11
MCQ (Multiple Correct Answer)

The Balmer series for the H -atom can be observed

A
if we measure the frequencies of light emitted when an excited atom falls to the ground state
B
if we measure the frequencies of light emitted due to transitions between excited states and the first excited state
C
in any transition in a H -atom
D
as a sequence of frequencies with the higher frequencies getting closely packed
12
MCQ (Multiple Correct Answer)

Let $E_n=\frac{-1 m e^4}{8 \varepsilon_0^2 n^2 h^2}$ be the energy of the $n$th level of H -atom. If all the H -atoms are in the ground state and radiation of frequency $\frac{\left(E_2-E_1\right)}{h}$ falls on it,

A
it will not be absorbed at all
B
some of atoms will move to the first excited state
C
all atoms will be excited to the $n=2$ state
D
no atoms will make a transition to the $n=3$ state
13
MCQ (Multiple Correct Answer)

The simple Bohr model is not applicable to $\mathrm{He}^4$ atom because

A
$\mathrm{He}^4$ is an inert gas
B
$\mathrm{He}^4$ has neutrons in the nucleus
C
$\mathrm{He}^4$ has one more electron
D
electrons are not subject to central forces
14
Subjective

The mass of a H -atom is less than the sum of the masses of a proton and electron. Why is this?

Explanation

Since, the difference in mass of a nucleus and its constituents, $\Delta M$, is called the mass defect and is given by

$$\Delta M=\left[Z m_p+(A-Z) m_n\right]-M$$

Also, the binding energy is given by $B=$ mass defect $(\Delta M) \times c^2$.

Thus, the mass of a H -atom is $m_p+m_e-\frac{B}{c^2}$, where $B \approx 13.6 \mathrm{eV}$ is the binding energy.

15
Subjective

Imagine removing one electron from $\mathrm{He}^4$ and $\mathrm{He}^3$. Their energy levels, as worked out on the basis of Bohr model will be very close. Explain why?

Explanation

On removing one electron from $\mathrm{He}^4$ and $\mathrm{He}^3$, the energy levels, as worked out on the basis of Bohr model will be very close as both the nuclei are very heavy as compared to electron mass.Also after removing one electron from $\mathrm{He}^4$ and $\mathrm{He}^3$ atoms contain one electron and are hydrogen like atoms.

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