The normalized ground-state wavefunction of a hydrogen atom is y(r)=(1/ra;)"2erl4 where a, = 53 pm (the Bohr radius) and r is the distance from the nucleus. (a) Calculate the probability that the electron will be found somewhere within a small sphere of radius 1.0 pm centred on the nucleus. (b) Now suppose that the same sphere is located at r = a,. What is the probability that the electron is inside it? You may approximate the probability of being in a small volume &V at position r by w(r) 8V.
The normalized ground-state wavefunction of a hydrogen atom is y(r)=(1/ra;)"2erl4 where a, = 53 pm (the Bohr radius) and r is the distance from the nucleus. (a) Calculate the probability that the electron will be found somewhere within a small sphere of radius 1.0 pm centred on the nucleus. (b) Now suppose that the same sphere is located at r = a,. What is the probability that the electron is inside it? You may approximate the probability of being in a small volume &V at position r by w(r) 8V.
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the answer is 1.21 × 10−6
please explain why
Transcribed Image Text:The normalized ground-state wavefunction of a hydrogen atom is
y(r)=(1/ra)"2eTl40 where a, = 53 pm (the Bohr radius) and r is the distance
from the nucleus. (a) Calculate the probability that the electron will be found
somewhere within a small sphere of radius 1.0 pm centred on the nucleus. (b)
Now suppose that the same sphere is located at r= a,. What is the probability
that the electron is inside it? You may approximate the probability of being in
a small volume &V at position r by y(r) 8V.
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