Question

1.

A) The element rubidium has a work function of 2.16 eV. What is the maximum kinetic energy of electrons if the metal is illuminated by light of wavelength 198 nm?

B) What is their speed?

2.

What wavelength light would have to fall on the metal tungsten (work function 4.55 eV) if it is to emit electrons with a maximum speed of 1.02x10⁶ m/s?

Answer 1

W = work function = 2.16 eV = 2.16 x 1.6 x 10-19 J = 3.46 x 10-19 J

= wavelength = 198 nm = 198 x 10-9 m

using the equation

max. kinetic energy = ( hc/ ) - W

max. kinetic energy = ( 6.6 x 10^-34 * 3 x 10⁸/ 198 x 10^-9 ) - 3.46 x 10^-19 J

max. kinetic energy = 10 x 10^-19 - 3.46 x 10^-19 J

max. kinetic energy = 6.54 x 10^-19 J

m = 9.1 x 10^-31 kg

so (0.5) m V² = 6.54 x 10^-19 J

(0.5) (9.1 x 10^-31) V² = 6.54 x 10^-19

V = 1.2 x 10⁶ m/s

B ) speed = V = 1.02 x 10⁶ m/s

m = 9.1 x 10^-31 kg

KEmax = (0.5) m V² = (0.5) (9.1 x 10^-31 kg) (1.02 x 10⁶ )² = 4.73 x 10^-19 J = 2.96 eV

max. kinetic energy = ( hc/ ) - W

2.96 = ( hc/ ) - 4.55

7.55 x 1.6 x 10^-19 = hc/

= hc / 7.55 x 1.6 x 10^-19

= (6.6 x 10^-34 * 3 x 10⁸ ) / 12.1 x 10-19

= 1.64 x 10^-7 = 164 nm