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Q. No.Photoelectrons emerging from a photocathode (work function: \(2.2~\text{eV}\)) are allowed to fall onto a gas containing hydrogen atoms in the ground state and the first excited state. What is the minimum energy of the photons incident on the photo-cathode that will cause the photoelectrons to transfer energy to the \(\mathrm{H\text-}\)atoms?
| 1. | \(13.6~\text{eV}+2.2~\text{eV}\) |
| 2. | \((10.2+2.2)~\text{eV}\) |
| 3. | \((3.4+2.2)~\text{eV}\) |
| 4. | \((1.89+2.2)~\text{eV}\) |
Subtopic: Â Photoelectric Effect: Experiment |
Level 4: Below 35%
Hints
When an electron makes a transition from the state \(n\) to \((n-1)\) the change in the de-Broglie wavelength of the electron: \(\Delta\lambda=|\lambda_n-\lambda_{n-1}|\)
varies with large \(n\) as:
varies with large \(n\) as:
| 1. | \(\dfrac{1}{n}\) | 2. | \(\dfrac{1}{n^2}\) |
| 3. | \(\dfrac{1}{n^4}\) | 4. | \(n^0,\text{ constant}\) |
Subtopic: Â De-broglie Wavelength |
Level 3: 35%-60%
Hints
The de-Broglie wavelength of a photon of energy \(E\) is \(\lambda_{ph}\) and that of an electron (non-relativistic) of the same energy \(E\) is \(\lambda_{e}.\) Then (assume \(E\text ~\)few \(e\text{V}\)):
1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
Subtopic: Â De-broglie Wavelength |
Level 3: 35%-60%
Hints
Photons of wavelength \(\lambda\) cause the emission of photoelectrons from a metallic surface, the de-Broglie wavelength of the fastest photoelectron being \(\lambda_d\). A graph of \(\dfrac{1}{\lambda} \text { vs } \dfrac{1}{\lambda_{d}}\) is:
| 1. | a straight line passing through the origin. |
| 2. | a circle. |
| 3. | an ellipse. |
| 4. | a parabola. |
Subtopic: Â De-broglie Wavelength |
Level 3: 35%-60%
Hints
Subtopic: Â Photoelectric Effect: Experiment |
Level 3: 35%-60%
Hints
All particles having a momentum of \(p\) are associated with wave-like behaviour and the wavelength, \(\lambda=h/p,\) where \(h\) is Planck's constant. Two particles \(A\) and \(B\) collide with each other, and come to rest. The de-Broglie wavelengths of \(A,B\) are \(\lambda_A,\lambda_B\) (before collision); while their masses are \(m_A,m_B.\) Then:
| 1. | \(\lambda_A=\lambda_B\) only if \(m_A=m_B\) |
| 2. | \(\lambda_Am_A=\lambda_Bm_B\) |
| 3. | \(\Large\frac{\lambda_A}{m_A}=\frac{\lambda_B}{m_B}\) |
| 4. | \(\lambda_A=\lambda_B,\) independent of \(m_A\) or \(m_B\) |
Subtopic: Â De-broglie Wavelength |
Level 3: 35%-60%
Hints
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:
| 1. | \(\propto\lambda_B\) | 2. | \(\propto{\Large\frac{1}{\lambda_B}}\) |
| 3. | \(\propto\lambda_B^{~2}\) | 4. | \(\propto{\Large\frac{1}{\lambda_B^{~2}}}\) |
Subtopic: Â De-broglie Wavelength |
Level 3: 35%-60%
Hints
During an experiment on the photoelectric effect, it was observed that (monochromatic light) photons incident on a photocathode, ejected electrons whose minimum de-Broglie wavelength was \(6.2~\mathring{A}.\) The work-function of the surface was \(1~\text{eV}.\) The energy of the incident photons was: \(\Bigg(\)one can use the formula \(\lambda_{dB}={\Large\frac{12.4}{\sqrt{E_k}}}\mathring{A}\Bigg)\)
1. \(101~\text{eV}\)
2. \(3~\text{eV}\)
3. \(4~\text{eV}\)
4. \(5~\text{eV}\)
1. \(101~\text{eV}\)
2. \(3~\text{eV}\)
3. \(4~\text{eV}\)
4. \(5~\text{eV}\)
Subtopic: Â Photoelectric Effect: Experiment |
Level 3: 35%-60%
Hints
In an experiment on the photoelectric effect, light of wavelength \(\lambda\) is used: but no photocurrent is observed, even when an accelerating voltage is applied to the cathode. Then, which of the following actions may cause a photocurrent?
| 1. | Increase in intensity of light |
| 2. | Increase in accelerating voltage |
| 3. | Decrease in the wavelength of light |
| 4. | Decrease in the intensity of light |
Subtopic: Â Photoelectric Effect: Experiment |
Level 3: 35%-60%
Hints
Photons of frequency \(\nu\) fill a room. A metallic plate having a work function \(W\) \((<h\nu)\) is moved with a velocity \(v\), in this room. The maximum energy of the emitted photoelectrons: (in the plate's frame)
| 1. | does not depend on \(v\) |
| 2. | increases as \(v\) increases |
| 3. | decreases as \(v\) increases |
| 4. | first increases and then decreases as \(v\) is increased |
Subtopic: Â Einstein's Photoelectric Equation |
 57%
Level 3: 35%-60%
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