Question

when light from a mercury lamp ( = 546.1 nm) is incident on a particular metal surface, the stopping potential is 0.974 v. (a) What is the work function (in eV) for this metal? eV

Answer 1

The work function of the metal is 0.9735 eV.

Step-by-step explanation:

The work function, denoted as Φ, is the minimum amount of energy required to remove an electron from the surface of a metal. The stopping potential, V0, is the voltage needed to prevent electrons from escaping the surface when illuminated by light.

To determine the work function of the metal, we can use the equation:

V0 = Φ/e

where e is the electronic charge, approximately 1.6 x 10^-19 C. Given the stopping potential V0 = 0.974 V, we can rearrange the equation to solve for Φ:

Φ = V0 * e

Substituting the values, we have:

Φ = 0.974 * 1.6 x 10^-19 C

Φ = 1.5584 x 10^-19 J

To convert this value to eV, we divide it by the electronic charge:

Work function = Φ / e

Work function = 1.5584 x 10^-19 J / 1.6 x 10^-19 C

Work function = 0.9735 eV

Answer 2

The work function for the metal is 1.520 eV.

Step-by-step explanation:

When light of a certain wavelength is incident on a metal surface, it can liberate electrons from the metal through the photoelectric effect. The stopping potential, measured in volts, is the minimum potential that must be applied to prevent these photoelectrons from reaching the anode. According to the photoelectric effect equation, the energy of the incident photons (E) is equal to the sum of the work function (Φ) and the kinetic energy of the emitted electrons (KE). Mathematically, this relationship is expressed as:

`\[E = eV_{\text{stopping}} = \Phi + KE\]`

where (e) is the elementary charge. Rearranging the equation to solve for the work function, we get:

`\[\Phi = eV_{\text{stopping}} - KE\]`

Since the electrons are brought to a stop, their kinetic energy becomes zero, and the equation simplifies to
`\(\Phi = eV_{\text{stopping}}\).`Substituting the given values, with the elementary charge
`\(e \approx 1.602 * 10^(-19)\)`C, and the stopping potential
`\(V_{\text{stopping}} = 0.974\)`V, we find:

`\[\Phi = (1.602 * 10^(-19) \, \text{C})(0.974 \, \text{V}) \approx 1.56 * 10^(-19) \, \text{J}\]`

Finally, converting this energy to electron volts (eV) by dividing by the elementary charge, we obtain the work function:

`\[\Phi = \frac{1.56 * 10^(-19) \, \text{J}}{1.602 * 10^(-19) \, \text{C/eV}} \approx 1.520 \, \text{eV}\]`

Therefore, the work function for the metal is approximately 1.520 eV.