Finding the energy of an electron from n=4 to n=2?

In summary, the conversation discusses finding the energy of a He+ electron transitioning from the n=4 state to the n=2 state. It also mentions the equation E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2\epsilon_0^2} for calculating energy levels, and the struggle to plug in the correct values for the variables.
  • #1
robertjordan
71
0

Homework Statement


Find the energy of a He+ electron going form the n=4 state to the n=2 state.


Homework Equations


E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2}
Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level.

^ I think those are the right meanings of the variables...

The Attempt at a Solution



I want to calculate E_4 and E_2 for He+ and compare the difference in their values, but I don't know what to plug in for everything to get an answer that makes sense. When I tried to use the E_n equation in one of my other homework problems, the units came out all wrong...

plugging in 1 for n, 3 for z, 9.11*10^-31 kg for m, -1.602*10^-19 Coulombs for e, and 1.054572×10^-34 J*s for h, we get
E_1= ((9.11*10^-31 kg))*((-1.602*10^-19 C)^4)*(3^2)/(2(1.054572×10^-34 J s)^2) = 2.428×10^-37 s^6A^4/(kg m^4) (second to the 6 amperes to the fourth per kilogram meter to the fourth).
 
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  • #2
Your equation for the energy is not correct. It should be [tex]E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2\epsilon_0^2}[/tex]

ehild
 

FAQ: Finding the energy of an electron from n=4 to n=2?

1. How do you calculate the energy of an electron from n=4 to n=2?

To calculate the energy of an electron moving from n=4 to n=2, you can use the formula E = -13.6 * (1/n2), where n is the principal quantum number. First, find the energy when n=4 and then when n=2. Subtract the two values to find the change in energy.

2. What is the significance of the n=4 and n=2 energy levels in an electron?

The energy levels n=4 and n=2 correspond to the fourth and second shells of an atom, respectively. As an electron moves from the fourth to the second shell, it releases energy in the form of a photon. This energy difference is important in understanding atomic structure and transitions.

3. How does the energy of an electron change as it moves from n=4 to n=2?

The energy of an electron decreases as it moves from n=4 to n=2. This is because the energy levels are closer together as the distance from the nucleus decreases. This results in a smaller energy difference between levels.

4. Can the energy of an electron moving from n=4 to n=2 be negative?

Yes, the energy of an electron can be negative when it moves from n=4 to n=2. This indicates that energy is being released from the electron as it transitions to a lower energy level.

5. How does the energy of an electron from n=4 to n=2 differ from other energy transitions?

The energy difference between the n=4 and n=2 levels is specific to the element and its atomic structure. Other energy transitions, such as n=3 to n=1, will have different energy differences due to the varying distances between energy levels.

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