A Hydrogen atom has one proton in the nucleus and one electron in the shell. In

Question

A Hydrogen atom has one proton in the nucleus and one electron in the shell. In a classic model of the atom, in a certain state, this electron is in a circular orbit around the nucleus with an velocity of 311637.102234259 m/s.

a)What is the radius of the orbit?

b) What is the angular momentum, L, of the electron at this radius?

c) What is the quantum value, n, of the electron at this radius?

d) What is the total energy of the electron at this radius?

e) What is the total energy of the electron at this radius in electron volts?

Explanation / Answer

mass of electron m = 9.1*10^-31 kg

charge = 1.6*10^-19 C

(a) from Bohr hydrogen model

v^2 = e^2/4pi*eo*mern

v = 311637.102234259

311637.102234259^2 = 9*10^9*(1.6*10^-19)^2/(9.1*10^-31*r)

rn = 2.607*10^-9 m

(b) L = mvr

L = 9.1*10^-31*311637.102234259*2.607*10^-9

L = 7.39*10^-34 kg.m^2/s

(c) mvr = nh/2pi

7.39*10^-34 = n*6.63*10^-34/6.28

n = 7

(d) En = -21.8*10^-18/n^2 J

E = -21.8*10^-18/7^2

E = -4.45*10^-19 J

(e) En = -13.6/n^2

E = -13.6/7^2

E = -0.278 eV

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