The radiation corresponding to \(3\rightarrow 2\) transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of \(3\times 10^{-4}~\text{T}\). If the radius of the largest circular path followed by these electrons is \(10.0~\text{mm}\), the work function of the metal is close to:
1. \(1.1~\text{eV}\)
2. \(0.8~\text{eV}\)
3. \(1.6~\text{eV}\)
4. \(1.8~\text{eV}\)

A nucleus \(A\), with a finite de-Broglie wavelength \(\lambda_A\), undergoes spontaneous fission into two nuclei \(B\) and \(C\) of equal mass. \(B\) flies in the same direction as that of \(A\), while \(C\) flies in the opposite direction with a velocity equal to half of that of \(B\). The de-Broglie wavelengths \(\lambda_B\) and \(\lambda_C\) of \(B\) and \(C\) are respectively:
1. \(\lambda_A,\frac{\lambda_A}{2}\)
2. \(\lambda_A,2\lambda_A\)
3. \(2\lambda_A, \lambda_A\)
4. \(\frac{\lambda_A}{2}, \lambda_A\)

The electric field of light wave is given as \(\vec{E}=10^{-3} \cos \left(\frac{2 \pi x}{5 \times 10^{-7}}-2 \pi \times 6 \times 10^{14} t\right) ~\text{N/C}\). This light falls on a metal plate of work function \(2~\text{eV}\). The stopping potential of the photo-electrons is:  \(\left(\text{Given,}~{E}~(\text {in } \text{eV})=\frac{12375}{\lambda~(\text{in } \mathring{\text{A}})}\right )\)
1. \(0.72~\text{V}\)
2. \(2.0~\text{V}\)
3. \(0.48~\text{V}\)
4. \(2.48~\text{V}\)

In a photoelectric effect experiment, the threshold wavelength of light is \(380~\text{nm}\). If the wavelength of incident light is \(260~\text{nm}\), the maximum kinetic energy of emitted electrons will be:
Given: \(E(\text {in}~\text{eV})=\dfrac{1237}{\lambda(\text {in}~ \text{nm})}\)
1. \(3.0~\text{eV}\)
2. \(1.5~\text{eV}\)
3. \(4.5~\text{eV}\)
4. \(15.1~\text{eV}\)

When radiation with a wavelength \(\lambda\) is used to illuminate a metallic surface, the stopping potential is \(V.\) However, when the same surface is illuminated with radiation of wavelength \(3\lambda,\) the stopping potential becomes \(\dfrac{V}{4}.\) The threshold wavelength for the metallic surface is:

When the wavelength of radiation falling on a metal is changed from \(500~\text{nm}\) to \(200~\text{nm}\), the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:
1. \(0.61~\text{eV}\)
2. \(0.81~\text{eV}\)
3. \(1.02~\text{eV}\)
4. \(0.52~\text{eV}\)

The stopping potential for electrons emitted from a photosensitive surface illuminated with light of wavelength \(491~\text{nm}\) is \(0.710~\text{V}.\) When the wavelength of the incident light changes, the stopping potential increases to \(1.43~\text{V}.\) The new wavelength is approximately:
1. \(329~\text{nm}\)
2. \(309~\text{nm}\)
3. \(382~\text{nm}\)
4. \(400~\text{nm}\)

Two streams of photons, with energies equal to twice and ten times the work function of the metal, are incident on its surface successively. The ratio of the maximum velocities of the photoelectrons emitted in these two respective cases will be: