Q. No.The frequency of the series limit of the Balmer series of hydrogen atoms in terms of the Rydberg constant \(R\) and velocity of light \(C\) is:
1. \(\frac{RC}{4}\)
2. \(RC\)
3. \(\frac{4}{RC}\)
4. \(4RC\)
(\(h = 6.626\times 10^{-34}\) J-s)
1. \(1.11\times 10^{34}~\text{J-s}\)
2. \(1.51\times 10^{-31}~\text{J-s}\)
3. \(2.11\times 10^{-34}~\text{J-s}\)
4. \(3.72\times 10^{-34}~\text{J-s}\)
1. \(n=4\)
2. \(n=2\)
3. \(n=16\)
4. \(n=3\)
A hydrogen atom is in an excited state of principal quantum number \((n)\). It emits a photon of wavelength \((\lambda)\) when it returns to the ground state. The value of \(n\) is:
1. \(\sqrt{\frac{\lambda R}{\lambda R-1}}\)
2. \(\sqrt{\frac{(\lambda R-1)}{\lambda R}}\)
3. \(\sqrt{\lambda(R-1)}\)
4. None of these
| 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. | \( \lambda_1=2\lambda_2=3 \lambda_3=\lambda_4\) |
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. \(2.92\times 10^{8}\) 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
In a Rutherford scattering experiment when a projectile of charge \(Z_1\) and mass \(M_1\) approaches a target nucleus of charge \(Z_2\)
and mass \(M_2\) the distance of the closest approach is \(r_0.\) What is the energy of the projectile?
| 1. | Directly proportional to \(M_1 \times M_2\) |
| 2. | Directly proportional to \(Z_1Z_2\) |
| 3. | Inversely proportional to \(Z_1\) |
| 4. | Directly proportional to the mass \(M_1\) |
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. \(3.4~\text{eV}\)
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 |
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