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Chapter 39: Q47P (page 1217)

For what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.00 mm? Assume that has its maximum value of n-1. (Hint:See Fig.39-24.)

Short Answer

Expert verified

The value of principal quantum number is 4.3脳103.

Step by step solution

01

Identification of the given data:

The given data is listed below as,

  • Radius of hydrogen atom isr=1.00mm=1.00脳10-3鈥�m
02

The principal Quantum number:

The principal quantum number is used to describe the electron鈥檚 state and is the one four quantum number assigned to each electron in an atom.

The value of the principal quantum number is natural number.

03

Determine the value of principal quantum number:

According to the fig. 39-24. the principal quantum number satisfies,

r=n2a

Here, the Bohr radius is a=5.29脳10-13鈥�m.

Solving the above equation will give the value of the principal quantum number is,

n=ra

Substitute 1.00脳10-3mfor r in the above equation.

n=1.00脳10-3m5.29脳10-13m=4.3脳103

Hence, the value of principal quantum number is 4.3脳103.

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