Determine the minimum potential that must be applied to a proton so that, on interaction with a hydrogen atom, it can excite the ground state electron to a state of n=3
please tell steps in brief
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To determine the minimum potential that must be applied to a proton, we need to consider the energy difference between the ground state and the desired state (n = 3) of the hydrogen atom. Here are the steps to calculate it:
1. Find the energy of the ground state of the hydrogen atom:
- The ground state energy of a hydrogen atom can be calculated using the equation: E = -13.6 eV / n^2, where n is the principal quantum number. For the ground state (n = 1), the energy is -13.6 eV.
2. Find the energy of the desired state (n = 3):
- Using the same equation, substitute n = 3 to find the energy of the third state: E = -13.6 eV / (3^2).
3. Calculate the energy difference:
- Subtract the energy of the ground state from the energy of the desired state to find the energy difference: ΔE = E(n=3) - E(n=1).
4. Convert the energy difference to joules:
- Use the conversion factor 1 eV = 1.6 × 10^-19 J to convert the energy difference from electron volts (eV) to joules (J).
5. Apply the minimum potential:
- The minimum potential applied to the proton must be equal to the energy difference calculated in step 4. The potential energy is given by the formula: V = ΔE / q, where q is the charge of the proton (1.6 × 10^-19 C).
By following these steps, you should be able to determine the minimum potential that must be applied to a proton to excite the ground state electron of a hydrogen atom to a state of n = 3.