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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.

16
Subjective

When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy?

Explanation

The transition of an electron from a higher energy to a lower energy level can appears in the form of electromagnetic radiation because electrons interact only electromagnetically.

17
Subjective

Would the Bohr formula for the H -atom remain unchanged if proton had a charge $(+4 / 3) e$ and electron a charge $(-3 / 4) e$, where $e=1.6 \times 10^{-19} \mathrm{C}$. Give reasons for your answer.

Explanation

If proton had a charge $(+4 / 3) e$ and electron a charge $(-3 / 4) e$, then the Bohr formula for the H -atom remain same, since the Bohr formula involves only the product of the charges which remain constant for given values of charges.

18
Subjective

Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

Explanation

According to Bohr model electrons having different energies belong to different levels having different values of $n$. So, their angular momenta will be different, as

$$L=\frac{n h}{2 \pi} \text { or } L \propto n$$