Q. No.If the de-Broglie wavelength of an electron in a Bohr orbit be \(\lambda_B,\) then the total energy in the \(n^{\text{th}}\) orbit is proportional to:
1.
\(\lambda_B\)
2.
\({\dfrac{1}{\lambda_B}}\)
3.
\(\lambda_B^{~2}\)
4.
\({\dfrac{1}{\lambda_B^{~2}}}\)
| 1. | \(\lambda_B\) | 2. | \({\dfrac{1}{\lambda_B}}\) |
| 3. | \(\lambda_B^{~2}\) | 4. | \({\dfrac{1}{\lambda_B^{~2}}}\) |
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| 1. | electrons emitted have a maximum kinetic energy of \(0.9~\text{eV}\) |
| 2. | electrons emitted have a maximum kinetic energy of \(2.9~\text{eV}\) |
| 3. | electrons emitted have a maximum kinetic energy of \(1.9~\text{eV}\) |
| 4. | electrons are not emitted |
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| 1. | \(\text{eV}/\mathring{A}\) | 2. | \(\text{eV}\text-\mathring{A}\) |
| 3. | \(\text{eV}\text-{\text s}\) | 4. | \(\text{eV}/{\text s}\) |
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1. \(101~\text{eV}\)
2. \(3~\text{eV}\)
3. \(4~\text{eV}\)
4. \(5~\text{eV}\)
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varies with large \(n\) as:
| 1. | \(\dfrac{1}{n}\) | 2. | \(\dfrac{1}{n^2}\) |
| 3. | \(\dfrac{1}{n^4}\) | 4. | \(n^0,\text{ constant}\) |
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When the path difference is changed by \(\delta,\) consecutive minima are observed in the neutron counting rates. This value of \(\delta\) is \(\Big(\hbar={\large\frac{h}{2\pi}},h=\text{Planck's constant}\Big)\):
| 1. | \({\Large\frac{h}{\sqrt{2mE}}}\) |
| 2. | \({\Large\frac{\hbar}{\sqrt{2mE}}}\) |
| 3. | \({\Large\frac{h}{2\sqrt{2mE}}}\) |
| 4. | \({\Large\frac{\hbar}{2\sqrt{2mE}}}\) |
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The phase difference between the neutrons in beam-\(1\) and beam-\(2\) due to the path difference is \(\Big(\hbar={\large\frac{h}{2\pi}}\Big)\):
| 1. | \({\Large\frac{\sqrt{2mE}}{\hbar}}(d_1-d_2)\) | 2. | \({\Large\frac{\sqrt{2mE}}{\hbar}\frac{(d_1-d_2)}{2}}\) |
| 3. | \({\Large\frac{\sqrt{2mE}}{\hbar}\frac{(d_1+d_2)}{2}}\) | 4. | \({\Large\frac{\sqrt{2mE}}{2\pi\hbar}}(d_1-d_2)\) |
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The wavelength of the neutrons is (\(h\)-Planck's constant):
| 1. | \(\Large{\sqrt\frac{mh^2}{2E}}\) | 2. | \(\Large{\sqrt\frac{h^2}{2mE}} \) |
| 3. | \(\Large{\sqrt\frac{2h^2}{mE}}\) | 4. | \(\Large{\sqrt\frac{2mh^2}{E}}\) |
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1. \(1~\text{eV}\)
2. \(2.5~\text{eV}\)
3. \(0.5~\text{eV}\)
4. \(4~\text{eV}\)
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