Determine the final end (final) value of n in a hydrogen atom transition, if electron starts in n = 1 and the atom absorbs a photon of light with an energy of 2.044 X 10^-18J?
A) 3
B) 4
C) 2
D) 6
E) 5
E = 2.180E-18 x (1/1 - 1/x)
Solve for x.
can someone show work for this problem ?
To determine the final value of n in a hydrogen atom transition, you need to use the formula for the energy of a photon absorbed or emitted during a hydrogen atom transition:
ΔE = 13.6 eV * (1/n_final^2 - 1/n_initial^2)
Where ΔE is the energy of the absorbed photon (2.044 X 10^-18 J in this case), n_initial is the initial value of n (1 in this case), and n_final is the final value of n (which we need to find).
Rearranging the formula, we can solve for n_final:
ΔE = 13.6 eV * (1/n_final^2 - 1/1^2)
ΔE = 13.6 eV * (1/n_final^2 - 1)
Now, substitute the given values into the equation and solve for n_final:
2.044 X 10^-18 J = 13.6 eV * (1/n_final^2 - 1)
To convert eV to joules, remember that 1 eV = 1.6 X 10^-19 J.
2.044 X 10^-18 J = 13.6 * (1/n_final^2 - 1)
2.044 X 10^-18 J = 13.6 * (1/n_final^2) - 13.6
2.044 X 10^-18 J + 13.6 = 13.6 * (1/n_final^2)
15.644 X 10^-18 J = 13.6/n_final^2
n_final^2 = 13.6/(15.644 X 10^-18 J)
n_final^2 = 8.697 X 10^17 J
n_final = sqrt(8.697 X 10^17)
n_final ≈ 2.95
Now, we need to round n_final to the nearest whole number, which is 3. Therefore, the final value of n is 3.
So, the correct answer is (A) 3.