The work function of a metal surface is Wo=4.80x10^-19 J. The maximum speed of t

Question

The work function of a metal surface is Wo=4.80x10^-19 J. The maximum speed of the electrons emitted from the surface is v_A=8.10 x 10^5 m/s when the wavelength is _A.  However a maximum speed of v_B = 5.10x10^5 m/s is observed when a wavelength _B is used.  What is the algebraic expression for wavelength? Express your answer in terms of h(Planck's constant=6.63x10^-34 J*s), c(3.00X(10^8 m/s), m (mass of electron=9.11x10^-31kg), Wo(working formula), and the maximum speed  (v_max) of an emitted electron.  What is the wavelength of _A and _B?

Explanation / Answer

from photo electric effect wnwergy of the photon E= W o + ( 1/ 2) m v ^ 2                                              ( hc / ) = W o + ( 1/ 2) m v ^ 2 from this wavelength   of light =hc / [ W o + ( 1/ 2) m v ^ 2 ]
for light of wavelength A , A = [ 6.625 * 10 ^ -34 * 3 * 10 ^ 8 ] / { [ 4.8 *10 ^ -19 ]+ [0.5 *9.11*10 ^ -31*(8.1*10^5)^2] }        = 255.182 * 10 ^ -9m        = 255.182 nm for light of wavelength B ,   B = [ 6.625 * 10 ^ -34 * 3 * 10 ^ 8 ] / { [4.8 * 10 ^ -19 ]+ [0.5 *9.11*10 ^ -31*(5.1*10^5)^2] }       = 332.09  * 10 ^ -9 m        = 332.09nm   B = [ 6.625 * 10 ^ -34 * 3 * 10 ^ 8 ] / { [4.8 * 10 ^ -19 ]+ [0.5 *9.11*10 ^ -31*(5.1*10^5)^2] }       = 332.09  * 10 ^ -9 m        = 332.09nm

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