For the ground state, also calculate √²P²), the root mean square of the electron's velocity, in terms of the speed of light c. Is the electron's speed non-relativistic? (Hint: You can utilize in position space that |P|² = −ħ²√². To simplify your result, you can use the where the fine structure constant is a = e² relation a = 2me 4πcohc ~ 1/137.) (Hydrogen atom dimensional analysis) In an energy eigenstate of the Hydrogen atom, the |P|² average kinetic energy and potential energy are of similar size, since (1²) = (-COT (T). One can use this relation to quickly determine expressions for the Bohr radius and the e² electron's r.m.s. velocity. Do so by assuming V² ~ -1/a² and in the 4περα expectation value relation above, to derive expressions for a and the electron's r.m.s. velocity. How close are these to the true expressions? (Note: this approach should get constants of e, me, ħ, c, eo correct, but might not get any dimensionless factors correct.) e2 Απεργ ħ amech
For the ground state, also calculate √²P²), the root mean square of the electron's velocity, in terms of the speed of light c. Is the electron's speed non-relativistic? (Hint: You can utilize in position space that |P|² = −ħ²√². To simplify your result, you can use the where the fine structure constant is a = e² relation a = 2me 4πcohc ~ 1/137.) (Hydrogen atom dimensional analysis) In an energy eigenstate of the Hydrogen atom, the |P|² average kinetic energy and potential energy are of similar size, since (1²) = (-COT (T). One can use this relation to quickly determine expressions for the Bohr radius and the e² electron's r.m.s. velocity. Do so by assuming V² ~ -1/a² and in the 4περα expectation value relation above, to derive expressions for a and the electron's r.m.s. velocity. How close are these to the true expressions? (Note: this approach should get constants of e, me, ħ, c, eo correct, but might not get any dimensionless factors correct.) e2 Απεργ ħ amech
Related questions
Question
100%
this is for hydrogen atom in ground state
Transcribed Image Text:For the ground state, also calculate √(P²), the root mean square of the electron's
velocity, in terms of the speed of light c. Is the electron's speed non-relativistic? (Hint: You
can utilize in position space that |P|² = −ħ²√². To simplify your result, you can use the
ħ
amech
~1/137.)
2me
e2
relation a =
where the fine structure constant is a =
4π€0ħc
(Hydrogen atom dimensional analysis) In an energy eigenstate of the Hydrogen atom, the
average kinetic energy and potential energy are of similar size, since (P1²) = -1/(-18²0 TT).
One can use this relation to quickly determine expressions for the Bohr radius and the
e²
electron's r.m.s. velocity. Do so by assuming V²
in the
4πεor
4περα
expectation value relation above, to derive expressions for a and the electron's r.m.s. velocity.
How close are these to the true expressions? (Note: this approach should get constants of
e, me, ħ, c, to correct, but might not get any dimensionless factors correct.)
e2
-1/a² and
Transcribed Image Text:2
1, V(r,0,0) = 33e¯r/ª YO(0, 6),
_r/a
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
