“Hydrogen-like helium” is helium with one outer electron stripped off. Leaving o

Question

“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 1.77 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

Force = k*q1q2/r^2
Where
Charge q1 = 2e
Charge q2 = -e
e = 1.6 * 10^-19 C
Radius r = 1.77 * 10^-11 m

(A) Inward Force , F = k*q1q2/r^2
F = 8.9 * 10^9 * 2e^2 / (1.77 * 10^-11)^2
F = 8.9 * 10^9 * 2(1.6*10^-19)^2 / (1.77 * 10^-11)^2
F = 1.454 * 10^-6 N

(B)
Force = mass * acceleration
Acceleration = Force/mass
Acceleration = (1.454 * 10^-6)/ (9.1 * 10^-31)
Acceleration = 1.6 * 10^24 m/s^2

(C)
Acceleration = v^2/r
Velocity, V = sqrt(a *r)
V = sqrt (1.6 * 10^24 *1.77 * 10^-11 )
V = 5.32 * 10^6 m/s
Velocity, V = 5.32 * 10^6 m/s

(D)
K.E = 0.5*m*v^2
K.E = 0.5*9.1*10^-31 * (5.32 * 10^6)^2 J
K.E = 1.287 * 10^-17 J
Kinetic Energy of Electron, K.E = 1.287 * 10^-17 J

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

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