Light of two different frequencies, whose photons have energies of \(1\) eV and \(2.5\) eV respectively, illuminates a metallic surface whose work function is \(0.5\) eV successively. The ratio of maximum speeds of emitted electrons will be:
1. \(1:2\)
2. \(1:1\)
3. \(1:5\)
4. \(1:4\)

A \(5~\text W\) emits monochromatic light of wavelength \(5000~\mathring{A}.\) When placed \(0.5~\text m\) away, it liberates photoelectrons from a photosensitive metallic surface. When the source is moved \(1.0~\text m\) away, the number of photoelectrons liberated is reduced by a factor of:
1. \(4\)
2. \(8\)
3. \(16\)
4. \(2\)

For photoelectric emission from certain metals, the cutoff frequency is \(\nu.\) If radiation of frequency \(2\nu\)$\mathrm{}$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be:
(\(m\) is the electron mass)

When the light of frequency \(2\nu_0\) (where \(\nu_0\) is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is \(v_1.\) When the frequency of the incident radiation is increased to \(5\nu_0,\) the maximum velocity of electrons emitted from the same plate is \(v_2.\) What will be the ratio of \(v_1\) to \(v_2?\)

An electron of mass \(m\) with an initial velocity \(\overrightarrow v= v_0\hat i\)$\stackrel{}{}$\( ( v_o > 0 ) \) enters in an electric field \(\overrightarrow E = -E_0 \hat i\) \((E_0 = \text{constant}>0)\) at \(t=0.\) If \(\lambda_0,\)${\mathrm{}}_{}$ is its de-Broglie wavelength initially, then what will be its de-Broglie wavelength at time \(t?\)

The figure shows different graphs between stopping potential \(V_0\) and frequency (\(\nu\)) for the photosensitive surfaces of cesium, potassium, sodium and lithium. The plots are parallel.
 

The value of stopping potential in the following diagram is given by:
    

The stopping potential for photoelectrons: