A sphere of work function `phi=4.6 eV` is suspended in a vacuum number by an insulating thread. Radiation of wavelength `lambda =0.2 mum` stricke on the sphere. The maximum electric pontential of the sphere will be

Options

A. 4.6 V
B. 6.2 V
C. 1.6 V
D. 3.2 V

Explanation

To solve the problem, we need to determine the maximum electric potential of a sphere when radiation strikes it, given its work function and the wavelength of the radiation. Here is a step-by-step solution:

### Step 1: Understand the photoelectric effect
The photoelectric effect states that when light of a certain frequency strikes a material, it can eject electrons from that material if the energy of the incoming photons is greater than the work function of the material.

### Step 2: Calculate the energy of the incoming photon
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant (\( 4.14 \times 10^{-15} \) eV·s),
- \( c \) is the speed of light (\( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength of the radiation.

Given:
- \( \lambda = 0.2 \, \mu m = 0.2 \times 10^{-6} \, m = 2000 \, \text{Å} \).

### Step 3: Substitute the values
Using \( \lambda = 2000 \, \text{Å} \):
\[ E = \frac{1240 \, \text{eV·nm}}{0.2 \, \mu m} \]
Convert \( \mu m \) to \( nm \):
\[ 0.2 \, \mu m = 200 \, nm \]
Now, substituting:
\[ E = \frac{1240 \, \text{eV·nm}}{200 \, nm} = 6.2 \, eV \]

### Step 4: Calculate the maximum kinetic energy of the ejected electrons
The maximum kinetic energy (KE_max) of the ejected electrons can be calculated using the formula:
\[ KE_{max} = E - \phi \]
where \( \phi \) is the work function of the material.

Given:
- \( \phi = 4.6 \, eV \)

Substituting the values:
\[ KE_{max} = 6.2 \, eV - 4.6 \, eV = 1.6 \, eV \]

### Step 5: Relate the maximum kinetic energy to the stopping potential
The stopping potential (V) is related to the maximum kinetic energy by:
\[ KE_{max} = eV \]
where \( e \) is the charge of an electron.

Rearranging gives:
\[ V = \frac{KE_{max}}{e} \]

Since the kinetic energy is already in electron volts, we can directly say:
\[ V = KE_{max} = 1.6 \, V \]

### Final Answer
The maximum electric potential of the sphere is **1.6 volts**.

---