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Problem 59 Hard Difficulty

How much energy is required to ionize a hydrogen atom when it is in (a) the ground state and (b) the $n=3$ state?

Answer

a) 13.6 $\mathrm{eV}$
b) 1.51 $\mathrm{eV}$

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Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Farnaz M.

Simon Fraser University

Video Transcript

for part A. We want to find the ionization and energy of hydrogen in the ground state which would be in equals one as well as in the n equals three state for part B. So the equation that governs this is getting written here on the right. This is the equation of ionization energy of atoms in different energy. Spit states specifically here for hydrogen. So this would be seven is equal. Toothy Coolum Constant case of B times The charge of them electron squared, divided by two A. Not where a non is the border radius multiplied by one over in squared where for part A is equal to one in is equal to three. So we simply just have to trust solve for these so east of one we just replaced that with equals one or within equals one. And this comes out to just be equal to kcb times he squared, divided by two times a not plugging these values and we find this is equal to 13.6 electron volts, which I'm sure you could have guessed since is the ground say energy of hydrogen atom? For part B, we replace that in value with three. So this is a three squared on the bottom. This is K City Times the charge of the electron square divided by two times a not multiplied by one over again, one over in squared, which is 1/3 squared or, in other words, one overnight playing these values in, we're just simply taking 13.6 TV and dividing it by nine. This comes out to equal 1.51 electron volts. That's our solution for party.

University of Kansas
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Farnaz M.

Simon Fraser University