Q. No.If an alpha nucleus of energy \(\frac{1}{2}mv^2\) bombards a heavy nuclear target of charge \(Ze\) then the distance of the closest approach for the alpha nucleus will be proportional to:
1.
\(\frac{1}{Ze} \)
2.
\(v^2 \)
3.
\(\frac{1}{m} \)
4.
\(\frac{1}{v^4}\)
| 1. | \(\dfrac{3}{23}\) | 2. | \(\dfrac{7}{29}\) |
| 3. | \(\dfrac{9}{31}\) | 4. | \(\dfrac{5}{27}\) |
1. \(0.5 \times 10^{7}~\text{m}^{-1}\)
2. \(0.25 \times 10^{7} ~\text{m}^{-1}\)
3. \(2.5 \times 10^{7}~\text{m}^{-1}\)
4. \(0.025 \times 10^{4} ~\text{m}^{-1}\)
An electron revolves around a nucleus of charge \(Ze\). In order to excite the electron from the state \(n=3\) to \(n=4\), the energy required is \(66.0 ~\text{eV}\).
The value of \(Z\) will be:
1. \(25\)
2. \(10\)
3. \(4\)
4. \(5\)
| 1. | total energy of electron in \(1\text{st}\) orbit of \(\mathrm{He}^{+}\) |
| 2. | total energy of electron in \(3\text{rd}\) orbit of \(\mathrm{He}^{+}\) |
| 3. | total energy of electron in \(2\text{nd}\) orbit of \(\mathrm{Li}^{++}\) |
| 4. | total energy of electron in \(3\text{rd}\) orbit of \(\mathrm{Li}^{++}\) |
1. \(1:1\)
2. \(1:2\)
3. \(1:4\)
4. \(2:1\)
| 1. | \(\dfrac{r_0}{9}\) | 2. | \(r_0\) |
| 3. | \(9r_0\) | 4. | \(3r_0\) |
| 1. | its potential energy increases and kinetic energy decreases. |
| 2. | its potential energy decreases and kinetic energy increases. |
| 3. | both kinetic energy and potential energy increase. |
| 4. | both kinetic energy and potential energy decrease. |
A beam of fast-moving alpha particles was directed towards a thin film of gold. The parts \(A', B',\) and \(C'\) of the transmitted and reflected beams corresponding to the incident parts \(A,B\) and \(C\) of the beam, are shown in the adjoining diagram. The number of alpha particles in:
| 1. | \(B'\) will be minimum and in \(C'\) maximum |
| 2. | \(A'\) will be the maximum and in \(B'\) minimum |
| 3. | \(A'\) will be minimum and in \(B'\) maximum |
| 4. | \(C'\) will be minimum and in \(B'\) maximum |
In the \(n^{th}\) orbit, the energy of an electron is \(E_{n}=-\frac{13.6}{n^2} ~\text{eV}\) for the hydrogen atom. What will be the energy required to take the electron from the first orbit to the second orbit?
1. \(10.2~\text{eV}\)
2. \(12.1~\text{eV}\)
3. \(13.6~\text{eV}\)
4. \(3.4~\text{eV}\)
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