finding frequency in chemistry problem

Question

A local FM radio station broadcasts at an energy of 6.12 * 10^-29 kJ/photon. (1 MHz=10^6 s^-1) Calculate the frequency at which it is broadcasting. Frequency = _____MHz

Answer 1

E = hv

E = energy = 6.12x10^-29 kJ

h = Planck's constant = 6.626x10^-34 J-sec

v = frequency = ?

Change units of energy to agree with units of Planck's constant.

6.12x10^-29 kJ x 1000 J / kJ = 6.12x10^-26 J

Solving for v (frequency) we have..

6.12x10^-26 J = (6.626x10^-34 J-sec)(v)

v = 6.12x10^-26 J / 6.626x10^-34 J-sec

v = 9.24x10⁷ sec^-1 = 9.24x10⁷ Hz

Converting to MHz, we have...

v = 9.24x10⁷ Hz x 1 MHz/10⁶ Hz = 92.4 MHz

Answer 2

E = h.f so. f = E/h = 6.12x10^-29 / 6.62x10^-34 = 9.2x10⁶ Hz = 9.2 MHz.

h = Planck constant = 6.62x10^-34 J.s.