Q. No.| 1. | \(\dfrac{r_0}{9}\) | 2. | \(r_0\) |
| 3. | \(9r_0\) | 4. | \(3r_0\) |
What is the ratio of the speed of an electron in the first orbit of an \(\mathrm{H}\text-\)atom to the speed of light?
| 1. | \(\dfrac{1}{137}\) | 2. | \(137\) |
| 3. | \(\dfrac{1}{83}\) | 4. | \(\dfrac{1}{47}\) |
The total energy of an electron in the first excited state of a hydrogen atom is about \(-3.4\) eV.
Its kinetic energy in this state will be:
1. \(-6.8~\text{eV}\)
2. \(3.4~\text{eV}\)
3. \(6.8~\text{eV}\)
4. \(-3.4~\text{eV}\)
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. \(3.4~\text{eV}\)
If an electron in a hydrogen atom jumps from the \(3\)rd orbit to the \(2\)nd orbit, it emits a photon of wavelength \(\lambda\). What will be the corresponding wavelength of the photon when it jumps from the \(4^{th}\) orbit to the \(3\)rd orbit?
| 1. | \(\dfrac{16}{25} \lambda\) | 2. | \(\dfrac{9}{16} \lambda\) |
| 3. | \(\dfrac{20}{7} \lambda\) | 4. | \(\dfrac{20}{13} \lambda\) |
| 1. | \(4 \lambda_1=2 \lambda_2=2 \lambda_3=\lambda_4\) |
| 2. | \( \lambda_1=2 \lambda_2=2 \lambda_3=\lambda_4\) |
| 3. | \( \lambda_1=\lambda_2=4 \lambda_3=9\lambda_4\) |
| 4. | \( \lambda_1=2\lambda_2=3 \lambda_3=\lambda_4\) |
| 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. |
1. \(1:1\)
2. \(1:2\)
3. \(1:4\)
4. \(2:1\)
1. \(n=4\)
2. \(n=2\)
3. \(n=16\)
4. \(n=3\)
Considering the \(3^{rd}\) orbit of \(\mathrm{He}^{+}\) (Helium ion), using the non-relativistic approach, the speed of the electron in this orbit will be: (Given: \(Z=2, K = 9\times 10^{9}\), and Planck's constant, \(h= 6.6\times10^{-34}\) J-s)
1. \(2.92\times 10^{8}\) m/s
2. \(1.46\times 10^{6}\) m/s
3. \(0.73\times 10^{8}\) m/s
4. \(3.0\times 10^{8}\) m/s
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