Solving the Bohr Model of Atom: Transition from n=7 to n=5

[Jodi]

Hi; Could someone please help me with this question: By what fraction does the mass of an H atom decrease when it makes an n=7 to n=5 transition? How would I go about this question? Thank you.

 

[MalleusScientiarum]

There's a mass change?

 

[Jodi]

I guess so. That's what confuses me about the question. I don't know how to incorporate the mass into it. Does anyone know how to do this? Thanks.

 

[James R]

What's the energy change?

Next, use $E=mc^2$.

 

[Jodi]

Ok, so I find the energy change by doing E of upper state - energy of lower state right? So I get (-0.2) - (-0.5) = 0.3 After I find this energy change, how do i find the decrease in mass? If I use E=mc^2, I plug in 0.3 into E and 1.00794 into m? What am I solving for? I'm confused. Thanks for your help.

 

[Dr.Brain]

As per $E=mc^2$ , Mass is the condensed form of energy . So whenever energy is released from particle , it is accompanied by a small mass change. So calculate the energy change from one state to another , and then equate the energy change with $mc^2$.

BJ

 

[James R]

You're trying to find m. c is the speed of light, which is $3 \times 10^8$ m/s. If you want m in kilograms, you need E in Joules. Your 0.3 is not in Joules, so you'll need to convert it.

If your energies are in eV, the conversion is: $1 eV = 1.6 \times 10^{-19} J$