Please show your work: “ Hydrogen-like helium ” is helium with one outer electro
ID: 1343074 • Letter: P
Question
Please show your work:
“Hydrogen-like helium” is helium with one outer electron stripped off. Leaving one outer electron stripped off, leaving one electron (charge e-) circling the nucleus containing two protons (charge 2e). (a) What is the inward force that the electron feels due to the positive charges in the nucleus, assuming that it orbits at a radius of 1.50 x 10^-11m? (b) If that electrical force causes the electron to follow a circular orbit, what is the electron’s centripetal acceleration? (c) What is the electron’s velocity? (d) What is the electron’s kinetic energy? (e) What is the electron’s potential energy U for this orbit? (f) What is the ratio of the potential energy to the kinetic energy?
Explanation / Answer
only 4 subparts at a time
a)
F= K*q1*q2/r^2
= (9*10^9)*(2*1.6*10^-19)*(1.6*10^-19) / (1.5*10^-11)^2
= 2.048*10^-6 N
b)
a = F/m
= 2.048*10^-6 / (9.1*10^-31)
=2.25*10^24 rad/s^2
c)
a = v^2/R
2.25*10^24 = v^2 / (1.5*10^-11)
v=5.81*10^6 m/s
d)
Kinetic energy = 0.5*m*v^2
= 0.5*(9.1*10^-31)*(5.81*10^6 )^2
=1.536*10^-17 J