(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Atoms are on the order of one Angstrom (A) or 10-10m in size while the diameter of the nucleus is approximately one hundred thousand times smaller. Let's pretend we have a "classical" atom where both the atom and its nucleus have a defined position and size. (This it contrary to the laws of quantum mechanics which appear to be true, but it's not a bad approximation.) Our atom has an diameter of 1 A and a nucleus that's 1.1 X10-15m in diameter. What is kinetic energy of a an electron whose de Brogile wave length is equal to the size of this atom?

2. Relevant equations

r1= nsquared*r

r2=nsquared*r

1/λ = R (1/(n1 squared) - 1/(n2 squared))

λ=hc/E

3. The attempt at a solution

r1= nsquared*r

(1.1E-15 m / 2)=nsquared*(5.29E-11 m)

n1=0.00322

r2=nsquared*r

(10E-10 m / 2)=nsquared*(5.29E-11 m)

n2=0.9722

1/λ = R (1/(n1 squared) - 1/(n2 squared))

1/λ = (10973731.6 inverse meters)(1/0.00322 squared - 1/0.9722 squared)

λ = 9.4485E-13

λ=hc/E

9.4485E-13 = (6.63E-34 J*s)(3E8 m/s) / E

E=2.1051E-13 J = 1314042.476 eV

Please help! I'm not even sure if I'm approaching the problem correctly.

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# Homework Help: De Broglie Waves

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