Question

The work function of the metal is 2.14 ev, and the stopping potential when light of 475 nm wavelength falls on the metal is 0.42 v. What is the threshold frequency of the metal?

1) 3.58 x 10¹⁴ Hz
2) 6.32 x 10¹⁴ Hz
3) 1.26 x 10¹⁵ Hz
4) 2.52 x 10¹⁵ Hz

Answer 1

The threshold frequency of a metal can be determined by using the work function and the energy of the incident light, subtracting the work function from the photon's energy, and relating it to the stopping potential using Einstein's photoelectric equation.

Step-by-step explanation:

To determine the threshold frequency of the metal, the energy of the incident light needs to be calculated, and the work function (energy needed to eject an electron) must be taken into account. By Einstein's photoelectric equation, Ephoton = Φ + K.E., where Ephoton is the energy of the incident photon, Φ is the work function, and K.E. is the maximum kinetic energy of the ejected electron. The stopping potential helps to find the K.E. of the ejected electrons, according to the equation K.E. = eV, where e is the elementary charge and V is the stopping potential.

First, calculate the energy of the incident photon using the equation E = (h⋅c) / λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light. Next, subtract the work function (in energy units, i.e., eV) from the photon energy to get the K.E. of the ejected electrons. Then, calculate the stopping potential needed to reduce the electrons' kinetic energy to zero. Once the stopping potential is known, we can solve the photoelectric equation to find the threshold frequency.

In this problem, the work function is given as 2.14 eV and the stopping potential as 0.42 V. The energy of the photon can be calculated using the given wavelength (475 nm). Hence, ignoring relativistic effects, the threshold frequency f0 = Φ / h. Substituting the value of the work function in eV and Planck's constant in eV⋅s, the threshold frequency of the metal can be estimated.