Final answer:
The energy required to change the energy state of the hydrogen atom electron from n=3 to n=4 is approximately 1.06 x 10^-19 J.
Step-by-step explanation:
The energy required to change the energy state of the hydrogen atom electron from n=3 to n=4 can be calculated using the equation:
E = -13.6 eV * (1/n2final - 1/n2initial)
Substituting the values, we get:
E = -13.6 eV * (1/42 - 1/32) = -13.6 eV * (1/16 - 1/9)
E = -13.6 eV * (9/144 - 16/144) = -13.6 eV * (-7/144)
E = 13.6 eV * (7/144) = 0.6633 eV
To convert from electron volts (eV) to joules (J), we use the conversion factor 1 eV = 1.602 x 10-19 J.
Therefore, the energy required is:
0.6633 eV * 1.602 x 10-19 J = 1.06 x 10-19 J