Q2) At time t = 0, a hydrogen atom is in the superposition state 4 Y(7, 0) = : e-r/ao +Ne-r/2a0(v5Y; + Y° – iY;')| (2a,)3/2 LV4 do a) Find the constant N so that Y(7, 0) is normalized. (Hint: First write it in terms of radial functions of hydrogen using Table 4.7) b) What is the possible results of a measurement of L? and with what probability of each? c) What is the possible results of a measurement of L, and with what probability of each? d) What is the radial probability density P,(r) that electron is found in a spherical shell located between the distances r and r + dr from the nucleus? e) At what value of r is P,(r) maximum? (Hint: a graphical method may help for the solution) f) Given the initial state ¥(†, 0), what is 4(†, t)? g) How do the answers to (a) to (e) depend upon time?
Q2) At time t = 0, a hydrogen atom is in the superposition state 4 Y(7, 0) = : e-r/ao +Ne-r/2a0(v5Y; + Y° – iY;')| (2a,)3/2 LV4 do a) Find the constant N so that Y(7, 0) is normalized. (Hint: First write it in terms of radial functions of hydrogen using Table 4.7) b) What is the possible results of a measurement of L? and with what probability of each? c) What is the possible results of a measurement of L, and with what probability of each? d) What is the radial probability density P,(r) that electron is found in a spherical shell located between the distances r and r + dr from the nucleus? e) At what value of r is P,(r) maximum? (Hint: a graphical method may help for the solution) f) Given the initial state ¥(†, 0), what is 4(†, t)? g) How do the answers to (a) to (e) depend upon time?
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Transcribed Image Text:Q2) At time t = 0, a hydrogen atom is in the superposition state
4
Y(7, 0) = :
e-r/ao +Ne-r/2a0(v5Y; + Y° – iY;')|
(2a,)3/2 LV4
do
a) Find the constant N so that Y(7, 0) is normalized. (Hint: First write it in terms of radial functions
of hydrogen using Table 4.7)
b) What is the possible results of a measurement of L? and with what probability of each?
c) What is the possible results of a measurement of L, and with what probability of each?
d) What is the radial probability density P,(r) that electron is found in a spherical shell located between
the distances r and r + dr from the nucleus?
e) At what value of r is P,(r) maximum? (Hint: a graphical method may help for the solution)
f) Given the initial state ¥(†, 0), what is 4(†, t)?
g) How do the answers to (a) to (e) depend upon time?
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