How much energy in joules is required to change the energy state of the H-atom electron from n=2 to n=3? from n=2 to n=4? from n=2 to infinity?
Kind of confused on this concept. Could you please explain for me? Thanks
dE = 2.18E-18(1/x^2 - 1/y^2)
Where x = 2 and y = 3 or
x = 2 and y = 4.
It's hard to write the formula on this forum which is why I used x and y; here is a try at the equation.
dE = 2.18E-18(1/n21 - 1/n32 where n1 is < n2
That 1/n^3 sub 2 should be
1/n^2 sub 2
Sure, I'd be happy to explain! To calculate the energy required to change the energy state of an electron in a hydrogen atom, we can use the formula:
E = -13.6 * (Z^2 / n^2) eV
where E is the energy in electron volts (eV), Z is the atomic number (which is 1 for hydrogen), and n is the principal quantum number of the energy state.
To convert this energy to joules, we multiply by the conversion factor 1 eV = 1.6 × 10^-19 Joules.
Let's calculate the energy required for each scenario you mentioned:
1. Change from n=2 to n=3:
First, calculate the energy difference between the two states:
ΔE = | E_n=3 - E_n=2 |
= |-13.6 * (1 / 3^2) - (-13.6 * (1 / 2^2)| eV
= |-13.6/9 + 13.6/4| eV
= |(-13.6*4 + 13.6*9)/(9*4)| eV
= 1.51 eV
Then, convert this energy to joules by multiplying by the conversion factor:
Energy in Joules = 1.51 eV * (1.6 × 10^-19 J/eV)
= 2.42 × 10^-19 J
Therefore, the energy required to change from n=2 to n=3 is approximately 2.42 × 10^-19 Joules.
2. Change from n=2 to n=4:
Similarly, calculate the energy difference:
ΔE = | E_n=4 - E_n=2 |
= |-13.6 * (1 / 4^2) - (-13.6 * (1 / 2^2)| eV
= |-13.6/16 + 13.6/4| eV
= |(-13.6*4 + 13.6*16)/(16*4)| eV
= 0.85 eV
Energy in Joules = 0.85 eV * (1.6 × 10^-19 J/eV)
= 1.36 × 10^-19 J
Therefore, the energy required to change from n=2 to n=4 is approximately 1.36 × 10^-19 Joules.
3. Change from n=2 to infinity:
As n approaches infinity, the energy difference between energy levels becomes negligible. In the limit of n reaching infinity, the energy required to change from n=2 to infinity is considered to be 0.
I hope this explanation helps clarify the concept! Let me know if you have any more questions.