Colliding hydrogen atoms find velocity to raise to N=2

[Bill Headrick]

Homework Statement

Two hydrogen atoms, both initially in the
ground state, undergo a head-on collision.
If both atoms are to be excited to the n = 2
level in this collision, what is the minimum
speed each atom can have before the collision?
Answer in units of m/s

1 mol of hydrogen is 1.008g

Homework Equations

En = K + Uelec

For a hydrogen atom: En= 13.6/N^2

The Attempt at a Solution

Okay, so I know that there is a change in energy that excites the atoms to N=2. This change in energy must be from kinetic energy.

So,
Two atoms collide into each other. And after the collision they are raised to N=2.

A. 2(Ei+K)=2(Ef) ;note, i used 2 because it is two atoms colliding
The twos cancel?
B. Ei+K=Ef
-13.6/(1*1)+1/2(mh)v^2=-13.6/(2*2) ;mh is mass of hydrogen
-13.6+1/2(mh)V^2=-3.4
C. 10.2=1/2(mh)v^2 ;add 13.6 to both sides

Am I correct up until here? (Part C)
To find mass of hydrogen
D. 1.008/6.02*10^23=1.67*10^-24

E. 10.2=1/2(1.67*10^-24)*(v^2)
20.4=(1.67*10^-24)*(V^2)
1.22155 E 25=V^2

Where did I mess up?

 

[Bill Headrick]

Okay, I figured it out:

10.2=1/2(mh)V^2
20.4=(mh)V^2

mh is equivalent to the mass of a proton which is 938E6 MeV/C^2

so, 20.4/938E6=v^2

so V^2 = 2.17484E-8
v= 1.474E-4

You have to multiply by c, I am not exactly sure the reasoning but
1.474E-4 * 299792458 = 44211.4107m/s

Hope if you stumble upon this with the same problem it helps.

Id still appreciate an explanation if anyone wants to give one.

 

[tms]

First, be clear that you are using the center of mass frame. In that frame, the situation with respect to the two H is symmetric, so you can just look at one of them.

Second, use the right units. Since you need your answer to be in MKS units, you need to convert the 13.6 eV to joules.

 

[tms]

mh is equivalent to the mass of a proton which is 938E6 MeV/C^2

You are off by a factor of a million.

Also, don't forget that in your energy balance equation the Hs still exist after the collision, so their masses are still there.

 

[Nickie]

Your approach is generally correct, but there are a few errors in your calculations. First, in part B, you have the correct equation but you have made a mistake in plugging in the values. The energy of the ground state is -13.6 eV, so when you plug it into the equation, it should be -13.6 eV, not -13.6. Also, the mass of hydrogen should be in kilograms, not grams, so you need to divide by 1000. Finally, in part D, you have made a mistake in calculating the mass of hydrogen. The mass of hydrogen is 1.008 grams per mole, but you need to convert it to kilograms, so it should be divided by 1000 and then multiplied by Avogadro's number (6.02 x 10^23). Once you fix these errors, you should get the correct answer for the velocity.