Calculate the energy change associated with the transition of an electron from the n=2 shell to the n=5 shell in a Bohr hydrogen atom.
4.6 × 10-19 J
dE= -Rh((1/nfinal^2)-(1/ninitial^2))
Rh is a constant = 2.178E^-18
The energy change associated with the transition of an electron from the n=2 shell to the n=5 shell in a Bohr hydrogen atom can be calculated using the formula:
ΔE = -R_H[(1/n_2^2) - (1/n_1^2)]
Where:
ΔE is the energy change
R_H is the Rydberg constant (2.18 x 10^-18 J)
n_1 is the initial shell number (n=2)
n_2 is the final shell number (n=5)
Plugging in the values:
ΔE = -R_H[(1/5^2) - (1/2^2)]
= -R_H[(1/25) - (1/4)]
= -R_H[(4 - 25)/100)]
= -R_H[-21/100]
= R_H[21/100]
The energy change associated with the electron transition from n=2 to n=5 is R_H[21/100].
To calculate the energy change associated with the electron transition from the n=2 shell to the n=5 shell in a Bohr hydrogen atom, we need to use the equation for the energy of an electron in the Bohr model:
E = -13.6eV/n^2
Where:
E is the energy of the electron,
n is the principal quantum number.
First, we need to determine the initial energy of the electron in the n=2 shell:
E_initial = -13.6eV/2^2 = -13.6eV/4 = -3.4eV
Next, we calculate the final energy of the electron in the n=5 shell:
E_final = -13.6eV/5^2 = -13.6eV/25 = -0.544eV
Now, we can find the energy change:
ΔE = E_final - E_initial = -0.544eV - (-3.4eV) = -0.544eV + 3.4eV = 2.856eV
Therefore, the energy change associated with the transition of an electron from the n=2 shell to the n=5 shell in a Bohr hydrogen atom is approximately 2.856 electron volts (eV).