# Finding velocity

1. Jul 31, 2011

### Saitama

1. The problem statement, all variables and given/known data
If the energy of H-atom in the ground state is -E, the velocity of the photo-electron emitted when a photon having energy EP strikes a stationary Li2+ ion in the ground state is given by:
(a)$v=\sqrt{\frac{2(E_P-E)}{m}}$
(b)$v=\sqrt{\frac{2(E_P+9E)}{m}}$
(c)$v=\sqrt{\frac{2(E_P-9E)}{m}}$
(d)$v=\sqrt{\frac{2(E_P-3E)}{m}}$

2. Relevant equations
E=W+K.E.
(W represents work function)

3. The attempt at a solution
Energy of H-atom in ground state, $E_H=-E$
Energy of Li+2 ion in ground state, $E_Li=-2.18*10^{-18}J*3^2=-9E$

$$K.E.=E-W$$
$$\frac{1}{2}mv^2=E_P-(-9E)$$
$$v=\sqrt{\frac{2(E_P+9E)}{m}}$$

2. Jul 31, 2011

### pmsrw3

The sign of the energy is a little confusing in this problem. Remember, energy is conserved, so the total energy before the photon is absorbed is that same as the total energy after. "Total" means you add all the relevant energies. But remember also that the energy of the atom before absorption of the photon is negative.

I would recommend that, instead of the photoelectric equation, you use the conservation of energy equation.

3. Jul 31, 2011

### Saitama

Sorry, i didn't get you.
Which is the conservation of energy equation?

4. Jul 31, 2011

### pmsrw3

Total energy before = total energy after

5. Aug 1, 2011

### Saitama

I know this but what formulae should i use here?

6. Aug 1, 2011

### Saitama

I have found the mistake in my solution.
-9E is the energy of Li2+ ion.
Therefore i need +9E energy to remove an electron.
So the work function becomes +9E rather than -9E and i get the answer as (c) option.

7. Aug 2, 2011

### I like Serena

Hi Pranav-Arora!

The energy before (initial energy Ei) is the energy of the photon plus the energy of the Lithium ion, which is Ei = Ep + (-9E).

The energy after (final energy Ef) is the kinetic energy of the electron plus the new energy of the Lithium ion, which is Ef = (1/2)mv2 + 0.

Energy conservation says Ei = Ef.
So Ep + (-9E) = (1/2)mv2 + 0.

From this you can deduce v.

8. Aug 2, 2011

### Saitama

Got it. Thanks for the explanation.