Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each transitions.?
n=4 => n=3 ? v = ________________ s^-1
n=5 => n=1 ?
n=5 => n=4 ?
n=6 => n=5 ?
I got the first one correct (1.6*10^14) but the rest i am getting wrong. Can anyone help me solve the last 3 questions?
You were probably doing it right. Frequencies just can’t be negative. So don’t add the negative sign.
#2
1/wavelength = R(1/1^2 - 1/5^2)
Then c = f*w and solve for f.
To calculate the frequency of light emitted when an electron in a hydrogen atom makes a transition, you can use the Rydberg formula:
1/λ = R_H * (1/n_final^2 - 1/n_initial^2)
where λ is the wavelength of light emitted, R_H is the Rydberg constant for hydrogen (approximately 1.097 × 10^7 m^-1), and n_initial and n_final are the initial and final energy levels of the electron, respectively.
To convert wavelength to frequency, you can use the equation:
v = c / λ
where v is the frequency, c is the speed of light in a vacuum (approximately 2.998 × 10^8 m/s), and λ is the wavelength.
Now let's calculate the frequencies for each of the given transitions:
1. For n=4 => n=3:
Using the Rydberg formula:
1/λ = R_H * (1/3^2 - 1/4^2)
= R_H * (1/9 - 1/16)
= R_H * (16/144 - 9/144)
= R_H * (7/144)
Now, convert the wavelength to frequency:
v = c / λ
= c / (R_H * (7/144))
Substitute the respective values:
v = (2.998 × 10^8 m/s) / (1.097 × 10^7 m^-1 * (7/144))
= (2.998 × 10^8 m/s) / (1.097 × 10^7 m^-1) * (144/7)
Simplify:
v ≈ 1.545 × 10^14 s^-1
So, the frequency of the light emitted when an electron transitions from n=4 to n=3 is approximately 1.545 × 10^14 s^-1.
2. For n=5 => n=1:
Using the Rydberg formula:
1/λ = R_H * (1/1^2 - 1/5^2)
= R_H * (1 - 1/25)
= R_H * (24/25)
Now, convert the wavelength to frequency as we did above.
v = c / λ
= c / (R_H * (24/25))
Substitute the respective values:
v = (2.998 × 10^8 m/s) / (1.097 × 10^7 m^-1 * (24/25))
Simplify to find the frequency.
3. For n=5 => n=4:
Using the Rydberg formula:
1/λ = R_H * (1/4^2 - 1/5^2)
= R_H * (1/16 - 1/25)
= R_H * (9/400)
Convert the wavelength to frequency as we did before.
4. For n=6 => n=5:
Using the Rydberg formula:
1/λ = R_H * (1/5^2 - 1/6^2)
= R_H * (1/25 - 1/36)
= R_H * (11/900)
Convert the wavelength to frequency as we did before.
Remember to substitute the values accurately while calculating, and you will get the correct frequencies for each transition.