Problem 29.37 PART A and B are answered please answer the other two Part A What

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Problem 29.37

PART A and B are answered please answer the other two

Part A What is the lowest possible energy (in electron volts) of an electron in hydrogen if its orbital angular momentum is 20? Express your answer in electronvolts to three significant figures.

En = -0.544 eV

Part B What is the largest value of the z component of the orbital angular momentum (in terms of ) for the electron in part A? Express your answer as an integer to one significant figure. Lz = 4

Part C What is the smallest value of the z component of the orbital angular momentum (in terms of ) for the electron in part A? Express your answer as an integer to one significant figure. Lz = m

Part D What is the largest value of the spin angular momentum (in terms of ) for the electron in part A? Express your answer using three significant figures. S = m

Part E What is the smallest value of the spin angular momentum (in terms of ) for the electron in part A? Express your answer using three significant figures. S = m SubmitMy AnswersGive Up Provide FeedbackContinue

Explanation / Answer

Part C

cos() = adjacent/hypotenuse
cos() = Lz /L
cos() = ml/[l(l +1)]½
cos() = ml /[l(l +1)]½

The smallest value for will correspond to the largest value of cos(). The largest value of cos() will occur where ml = l and where l has its maximum value: 4.

cos() = 4/[4(4 +1)]½
cos() = 4/2*(5)½
cos() = 25 = .8944272
= 26.565°

Part D

n=5 (pretty much irrelevant)

The f tells you that the orbital angular momentum is l=3

So the z-component of orbital angular momentum (ml) can run from -3 to 3.

The spin angular momentum is s=1/2.

So the total angular momentum can be:
j = l + or -s
= 5/2 or 7/2.

So the maximum z-component of angular momentum (mj) would be 7/2.

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