What is the kinetic energy, in eV, of a free (unbound) electron that has deBrogl

Question

What is the kinetic energy, in eV, of a free (unbound) electron that has deBroglie wavelength 80.0 nm? b) What is the energy, in eV, of a photon that has wavelength 80.0 nm? c) A photon has linear momentum 8.00 times 10^-25 kg middot m/s and energy 1500 eV. What is the energy of the photon if its momentum is doubled, so that the momentum of the photon is 16.0 times 10^-25 kg middot m/s? d) A photon has linear momentum 8.00 times 10^-25 kg middot m/s and wavelength 0.828 nm. What is the wavelength of the photon if its momentum is doubled, so that the momentum of the photon is 16.0 times 10^-25 kg m/s.

Explanation / Answer

a) lamda = 80nm

lamda = h/mv = h/(2mK)^0.5

80*10^-9 = 6.63*10^-34/(2*9.1*10^-31*K)^0.5

K = 3.774*10^-23 J

K = 3.774*10^-23/(1.6*10^-19)

K = 0.00024 eV

(b) E = hc/lamda

E(eV)=1243/lamda(nm)

E =1243/80

E = 15.54 eV

(c) p^2 = 2mK

(p2/p1)^2 = K2/K1

(2)^2 = K2/1500

K2 = 6000 eV

(d) lamda = h/p

lamda2/lamda1 = p1/p2

lamda2/0.828 = 1/2

lamda2= 0.414 nm

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