In a photoelectric effect experiment you illuminate a metal with light of an unknown wavelength and measure the maximum kinetic energy of the photoelectrons to be 0.65 eV. Then you illuminate the same metal with light of a wavelength known to be 2/3 of the first wavelength and measure a maximum kinetic energy of 1.9 eV for the photoelectrons. 1. Find the first wavelength, in nanometers. lambda_1 = 2. Find the metal's work function, in electron volts.

1. λ₁ = 4.97 x 10⁻⁷ m = 497 nm

2. ∅ = 3.96 x 10⁻¹⁹ J = 2.475 eV

Explanation:

Using Einstein's Photoelectric Equation:

Energy Given by Photon = Work Function + K.E of Electron

hc/λ = ∅ + K.E

where,

h = Plank's Constant = 6.63 x 10⁻³⁴ J.s

c = speed of light = 3 x 10⁸ m/s

λ = wavelength of light

∅ = work function

K.E = Kinetic Energy of Electron

FOR 1ST SCENARIO:

K.E = 0.65 eV

Therefore,

hc/λ₁ = ∅ + 0.65 eV   equation 1

FOR 2ND SCENARIO:

λ₂ = (2/3)λ₁

K.E₂ = 1.9 eV

Therefore,

hc/(2/3)λ₁ = ∅ + 1.9 eV  

(3/2)hc/λ₁ = ∅ + 1.9 eV   equation 2

1.

Subtracting equation 1 from equation 2, we get:

(3/2)hc/λ₁ - hc/λ₁ = ∅ + 1.9 eV - ∅ - 0.65 eV  

(1/2)hc/λ₁ = 1.25 eV

(1/2)(6.63 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/λ₁ = (1.25 eV)(1.6 x 10⁻¹⁹ J/1 eV)

λ₁ = (9.945 x 10⁻²⁶ J.m)/(2 x 10⁻¹⁹ J)

λ₁ = 4.97 x 10⁻⁷ m = 497 nm

2.

Using values in equation 1:

(6.63 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(4.97 x 10⁻⁷ m) = ∅ + (0.65 eV)(1.6 x 10⁻¹⁹ J/1 eV)

4 x 10⁻¹⁹ J - 1.04 x 10⁻¹⁹ J = ∅

∅ = 3.96 x 10⁻¹⁹ J = 2.475 eV

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.