Light of wavelength 180nm strikes a metal target and photoelectrons are emitted. It is noticed that the photocurrent drops to zero at stopping potential of 0.8 V. The work function of the metal surface is___________a.None of theseb.5.03 eVc.6.09 eVd.3 eVe.3.7 eV

To solve this problem, we need to use the photoelectric effect equation:

E = hf - Φ

where E is the energy of the emitted photoelectron, h is Planck's constant, f is the frequency of the incident light, and Φ is the work function of the metal.

First, we need to convert the wavelength of the light to frequency using the equation:

f = c/λ

where c is the speed of light (3 x 10^8 m/s) and λ is the wavelength. The wavelength needs to be in meters, so we convert 180 nm to 180 x 10^-9 m.

f = (3 x 10^8 m/s) / (180 x 10^-9 m) = 1.67 x 10^15 Hz

Next, we can calculate the energy of the photoelectron using the stopping potential. The energy is given by:

E = eV

where e is the charge of an electron (1.6 x 10^-19 C) and V is the stopping potential (0.8 V).

E = (1.6 x 10^-19 C)(0.8 V) = 1.28 x 10^-19 J

Now we can solve for the work function Φ:

Φ = hf - E

Substituting the values we have:

Φ = (6.63 x 10^-34 J.s)(1.67 x 10^15 Hz) - 1.28 x 10^-19 J = 1.28 x 10^-19 J

Converting this to electron volts (eV) by dividing by the charge of an electron:

Φ = 1.28 x 10^-19 J / 1.6 x 10^-19 C = 0.8 eV

So, the work function of the metal surface is not listed in the options provided. The correct answer is "None of these".

To solve this problem, we need to use the photoelectric effect equation:

E = hf - Φ

where E is the energy of the emitted photoelectron, h is Planck's constant, f is the frequency of the incident light, and Φ is the work function of the metal.

First, we need to convert the wavelength of the light to frequency using the equation:

f = c/λ

where c is the speed of light (3 x 10^8 m/s) and λ is the wavelength. The wavelength needs to be in meters, so we convert 180 nm to 180 x 10^-9 m.

f = (3 x 10^8 m/s) / (180 x 10^-9 m) = 1.67 x 10^15 Hz

Next, we calculate the energy of the photoelectron using the stopping potential. The energy is given by:

E = eV

where e is the charge of an electron (1.6 x 10^-19 C) and V is the stopping potential.

E = (1.6 x 10^-19 C)(0.8 V) = 1.28 x 10^-19 J

Now we can solve for the work function Φ:

Φ = hf - E

Substituting the values we have:

Φ = (6.63 x 10^-34 J.s)(1.67 x 10^15 Hz) - 1.28 x 10^-19 J = 9.28 x 10^-19 J

To convert this to electron volts (eV), we divide by the charge of an electron:

Φ = (9.28 x 10^-19 J) / (1.6 x 10^-19 C) = 5.8 eV

So, the work function of the metal surface is not listed in the options provided. The correct answer should be "None of these".