Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n=3 to n=1 energy level, based on the Bohr theory. use the equation En=
-2.18 x10-18 J(1/n2)
To calculate the frequency of the light emitted by a hydrogen atom during a transition from the n=3 to n=1 energy level, we can use the equation for the energy levels of the hydrogen atom based on the Bohr theory. The equation is:
En = -2.18 x 10^-18 J * (1/n^2)
where En is the energy level, n is the principal quantum number, and -2.18 x 10^-18 J is the Rydberg constant for hydrogen.
In this case, we are given that the electron transitions from the n=3 to n=1 energy level. So we can substitute those values into the equation:
E3 = -2.18 x 10^-18 J * (1/3^2)
E1 = -2.18 x 10^-18 J * (1/1^2)
To find the frequency of the light emitted, we can use the equation:
E = h * f
where E is the energy of the emitted light, h is Planck's constant (6.63 x 10^-34 J·s), and f is the frequency of the light.
We can rearrange the equation to solve for f:
f = E / h
Substituting the energy values we calculated earlier:
f = (E3 - E1) / h
Now, we can calculate the frequency:
f = (-2.18 x 10^-18 J * (1/3^2) - (-2.18 x 10^-18 J * (1/1^2))) / (6.63 x 10^-34 J·s)
Simplifying the expression:
f = (-2.18 x 10^-18 J * (1/9) + 2.18 x 10^-18 J) / (6.63 x 10^-34 J·s)
f = (-2.18 x 10^-18 J / 9 + 2.18 x 10^-18 J) / (6.63 x 10^-34 J·s)
f = (-2.42 x 10^-19 J + 2.18 x 10^-18 J) / (6.63 x 10^-34 J·s)
f ≈ 3.09 x 10^15 Hz
Therefore, the frequency of the light emitted by the hydrogen atom during the transition is approximately 3.09 x 10^15 Hz.
To calculate the frequency of the light emitted during a transition of an electron in a hydrogen atom from the n=3 to n=1 energy level, we can use the equation:
En = -2.18 x 10^−18 J * (1/n2)
First, let's find the energy difference between the two energy levels.
ΔE = Efinal - Einitial
Given:
Einitial = En=3
Efinal = En=1
Plugging these values into the equation, we have:
ΔE = (-2.18 x 10^−18 J) * (1/1^2) - (-2.18 x 10^−18 J) * (1/3^2)
Simplifying this expression, we get:
ΔE = (-2.18 x 10^−18 J) * (1 - 1/9)
ΔE = (-2.18 x 10^−18 J) * (8/9)
ΔE = -1.957 x 10^−18 J
Next, let's use the equation to calculate the frequency (ν) of the light emitted during the transition:
ΔE = h * ν
Given that the Planck's constant (h) is approximately 6.626 x 10^−34 J·s, we can rearrange the equation to solve for the frequency:
ν = ΔE / h
Plugging in the values, we get:
ν = (-1.957 x 10^−18 J) / (6.626 x 10^−34 J·s)
ν ≈ -2.956 x 10^15 Hz
Therefore, the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n=3 to n=1 energy level is approximately -2.956 x 10^15 Hz.