When light of wavelength, 215 nm, impinges a photocathode that has a binding ene

Question

When light of wavelength, 215 nm, impinges a photocathode that has a binding energy of 2.19 eV, electrons are ejected. What is the speed (in m/s) of the ejected electrons? h = 6.626 x 10–34J·s, c = 2.9979 x 108m/s, 1 eV = 1.602 x 10–19 J, NA= 6.022 x 1023mol–1, me = 9.11 x 10–31 kg, KE = ½ mv2. Report your answer to three significant figures. It might be easier to enter your answer in scientific notation. So, for example, if your answer is 923672, in scientific notation and to 3 significant figures, the number is 9.24 x 105and you would enter 9.24e5.

and

When light of wavelength of a certain wavelength impinges a photocathode that has a binding energy of 3.5 eV, electrons are ejected. What is the wavelength (in nm) of the light if the kinetic energy of one ejected electron is 4.8 x 10–19J? h = 6.626 x 10–34J·s, c = 2.9979 x 108m/s, 1 eV = 1.602 x 10–19 J, NA= 6.022 x 1023mol–1. Report your answer to three significant figures.

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Explanation / Answer

a.

Ek = hc/ W = mv2 /2

6.626 ×1034 J.s x 2.9979 x 108 m. s-1 /215x10-9m – 2.19eVx1.602 x10-19 J/eV =

     = 9.11 x 10–31 kg x v2 / 2

(9.24x10-19 J – 3.51x10-19 J)/ 9.11 x 10–31 kg = v2 / 2

2 x 6.29 x 1011 J/kg = v2

v = 1.12x106 m/s

b.

Ek = hc/ W

= hc / (Ek + W)

= 6.626 ×1034 J.s x 2.9979 x 108 m. s-1 / (4.8 x 10–19J + 3.5eVx1.602 x10-19J/eV

= 1.986x10-25 J.m/ 1.041x10-18 J = 1.91x10-7m = 191x10-9 m= 191 nm

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