As the principle quantum number increases, the electron is more likely to be fou

Question

As the principle quantum number increases, the electron is more likely to be found far from the nucleus. It can be shown that for hydrogen-like atoms, the expectation value of r,

(a) Calculate the value of n (round up to the nearest integer) for an s-state in the hydrogen atom such that <r>=486 a0.

(b) What is the ionization energy of H atom in this state in electron volts?

(c) Compare your answer with the ionization energy of hydrogen atom in the ground state.

Please give step by step on how to solve and show work please, struggling need to understand how to do it as well

Explanation / Answer

a) s state means l= 0

so <r? = n^2 a0/Z(1 + 1/2)

hydrogen so Z = 1

<r> = n^2*3/2 a0 = 486 a0

n = sqrt(486*2/3)= 18

b) E = -13.6/n^2 = -13.6/18^2=-0.0420

c) it is much larger than the ground state of -13.6 eV

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.