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(25%) Problem 4: In this problem, we ask two questions about the motion of the e

ID: 2038296 • Letter: #

Question

(25%) Problem 4: In this problem, we ask two questions about the motion of the electron in the Bohr model of the hydrogen atom when the atom is in its N-th energy level, which is the (N - 1)-th excited state above the ground state ? 50% Part(a) Calculate the magnitude of the translational ( orbital) angular momentum ofthe electron about the prolon in the Bohr model of the hydrogen atom when the atom is int its N-th cncrgy level with N- 5. Express your answer in units of kg mis Final Grade 100% Correct Answer Student Answer I. 5.278* 10-34 I 5.278T-34 T.- 5.273T-34 Grade Detail Correct Student Feedback Final Answer Credit 100% Submission Historv ITints Feedback Totals 0% Answer 0% L-5.27810-34 L-5.278E-34 0% 0% Totals 0% 0% 0% 0% a 50% Part(b) In the Bohr model of the hydrogen atom the radius of the electron's orbit when the atom is in its N th energy level is given by r = N ao where ao denotes the Bohr radius, whose value is approximately ao 5.29 × 10-11 m. Use that relation to find the speed of the electron in its orbit, in meters per second, when the atom is at its N-th energy level with N.

Explanation / Answer

a) In N = 5th orbit,

L = N*h/(2*pi)

= 5*6.626*10^-34/(2*pi)

= 5.27*10^-34 kg.m^2/s

b) radius of Nth orbit, r = ao*N^2

= 5.29*10^-11*5^2

= 1.322*10^-9 m

we know, L = m*v*r

v = L/(m*r)

= 5.27*10^-34/(9.1*10^-31*1.322*10^-9)

= 4.38*10^5 m/s