An electron initally at rest is accelerated by a potential of 12 V. It then coll

Question

An electron initally at rest is accelerated by a potential of 12 V. It then collides with a hydrogen atom at rest in the n=1 state. After the collision the atom is left in the n=2 state. (A) What is the kinetic energy and the wavelength of the electron before it hits the atom? (B) After the collision the atom decays from the n=2 state down to the n=1 state, and emits a photon. What is the wavelength of the photon? (C)What is the velocity of the electron after the collision? The kinetic energy of the atom after the collision is very small and can be neglected.

Explanation / Answer

Here ,

potential difference , V = 12 V

a)

kinetic energy of electron = 12 * 1.602 *10^-19

kinetic energy of electron = 1.923 *10^-18 J

the kinetic energy of electron is 1.923 *10^-18 J

wavelength = h/(sqrt(2 * m * KE))

wavelength = 6.626 *10^-34/(sqrt(2* 9.11 *10^-31 *1.923 *10^-18 ))

wavelength = 3.54 *10^-10 m

the wavelength is 3.54 *10^-10 m

B)

for the wavelength

h*c/(wavelength * e) = 13.6 * (1/1^2 - 1/2^2)

6.626 *10^-34 * 3 *10^8/(wavelength * 1.602 *10^-19) = 13.6 * (1/1^2 - 1/2^2)

solving for wavelength

wavelength = 1.216 *10^-7 m

the wavelength of light emitted is 1.216 *10^-7 m

c)

final kinetic energy = initial kinetic energy - energy of photon emitted

0.5 * 9.11 *10^-31 * v^2 = (12 - 13.6 *(1/1^2 - 1/2^2)) * 1.602 *10^-19

solving for v

v = 7.95 *10^5 m/s

the speed of electron after the collision is 7.95 *10^5 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.