The mathematical equation for studying the photoelectric effect is hv = W + 1/2

Question

The mathematical equation for studying the photoelectric effect is hv = W + 1/2 m_1u^2 where v is the frequency of light shining on the metal; W is the energy needed to remove an electron from the metal: and m_e and u are the mass and speed of the ejected electron, respectively. In an experiment, a student found that a maximum wavelength of 381 nm is needed to just dislodge electrons from a metal surface. Calculate the velocity (in m/s) of an ejected electron when the student employed light with a wavelength of 303 nm. 6.734 m/s

Explanation / Answer

The equation for photo electric effect is

hv = w + 1/2 mv2

where w= work function = hvo we know that frequency = c/ wavelength

Given the threshold wavelength = 381 nm = 381x10-9 m

and the wavelngth used = 303x10-9 m

Thus

(6.623x10-34J.s x3x108m/s)/303x10-9 m = (6.623x10-34J.s x3x108m/s)/381x10-9 m +1/2 [9.11x 10-31kg V2]

solving for Velocity we get V = 2.945x 105m/s

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