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 1090729.85781991 m/s. What is the radius of the orbit? What is the angular momentum, L, of the electron at this radius? What is the quantum value, n, of the electron at this radius? What is the total energy of the electron at this radius? What is the total energy of the electron at this radius in electron volts? Solution velocity, v=10.9073*10^5 m/sec a) use, m*v^2/r = k*q1*q2^2/r^2 m*v^2 = k*e^2/r 9.11*10^-31*(10.9073*10^5)^2=9*10^9*(1.6*10^-19)^2/r ===> r=2.126*10^-10 m or 0.2126nm b) angular momentum, L=m*v*r =9.11*10^-31*10.9073*10^5*2.126*10^-10 =2.11*10^-34 J.sec c) use, L=n*h/2pi 2.11*10^-34=n*6.626*10^-34/(2pi) ==> n=2 quantum value, n=2 d) K.E=1/2*m*v^2 =1/2*9.11*10^-31*(10.9073*10^5)^2 =5.42*10^-19 J total energy, T.E=-K.E T.E=-5.42*10^-19 J a) T.E=-5.42*10^-19 *6.24*10^18 T.E=-3.4 ev .

1. 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 1090729.85781991 m/s.
What is the radius of the orbit?
What is the angular momentum, L, of the electron at this radius?
What is the quantum value, n, of the electron at this radius?
What is the total energy of the electron at this radius?
What is the total energy of the electron at this radius in electron volts?
Solution
velocity, v=10.9073*10^5 m/sec
a)
use,
m*v^2/r = k*q1*q2^2/r^2
m*v^2 = k*e^2/r
9.11*10^-31*(10.9073*10^5)^2=9*10^9*(1.6*10^-19)^2/r
===> r=2.126*10^-10 m or 0.2126nm
b)

2. angular momentum, L=m*v*r
=9.11*10^-31*10.9073*10^5*2.126*10^-10
=2.11*10^-34 J.sec
c)
use,
L=n*h/2pi
2.11*10^-34=n*6.626*10^-34/(2pi)
==> n=2
quantum value, n=2
d)
K.E=1/2*m*v^2
=1/2*9.11*10^-31*(10.9073*10^5)^2
=5.42*10^-19 J
total energy, T.E=-K.E
T.E=-5.42*10^-19 J
a)

3. T.E=-5.42*10^-19 *6.24*10^18
T.E=-3.4 ev