# Electron transition question

E of nlow to nhigh= -2.178*10^-18 * Z^2/nhigh^2 - nlow^2

find the energy needed to remove an electron completely from a hydrogen atom and the energy needed to remove one mol of electrons from one mol of hydrogen atoms

Z= 1 nhigh= infinity nlow=1

E = 2.178*10^-18 J
one mole of electrons = 2.178*10^-18 * 6.022*10^23 = 1.312*10^6 J/mol
Are these right??

And use the above formula to find the value of Z for an ion whose 2 to 1 transition is associated with a wavelength of 13.4nm.

lamba of 2 to 1= hc/(2.178*10^-18 * Z^2/nhigh^2 - nlow^2)
z=sqrt(hc(nhigh^2-nlow^2)/(13.4*10^-9)(2.178*10^-18))
Z= 4.5
or 5
Is this right??

Thank you guys so much for your help.
Stephen

Borek
Mentor
E of nlow to nhigh= -2.178*10^-18 * Z^2/nhigh^2 - nlow^2

Try to use TEX or at least brackets, it doesn't look OK at the moment.

Redbelly98
Staff Emeritus
Homework Helper
Hello Stephen,

Looks good on the single hydrogen atom and mole-of-hydrogen question.

But it looks like there's an error somewhere in the Z question. The correct answer is very close to an integer.

I think the problem is with the expressions you are writing. There should be a term

( 1/nhigh^2 - 1/nlow^2 )​

nhigh^2 - nlow^2​

???

Regards,

Mark

p.s. Borek is correct, it's better to at least use brackets (parantheses) to express things properly and avoid confusion.

Z^2/nhigh^2 - nlow^2
is the same thing as z^2*(1/nhigh^2 - 1/nlow^2)

Redbelly98
Staff Emeritus
Homework Helper

z = sqrt(...)​

it has mysteriously become, literally,

(nhigh^2-nlow^2)​

and that is wrong.

Try keeping it as

(1/nhigh^2 - 1/nlow^2)​

Also, you might find it easier to figure out what the energy is for 13.4 nm, and then work with the energy equation (1st equation of your 1st post).