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find the frequency of light f radiated by an electron moving from orbit n1=2 to n2=1 inside of a he ion.

User Jayj
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2 Answers

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Final answer:

To find the frequency of light emitted by an electron moving from orbit n=2 to n=1 inside of a He+ ion, the Bohr model and Planck's equation are used to calculate the energy difference between orbits and thereby find the photon's frequency.

Step-by-step explanation:

Calculating the Frequency of Light in a Helium Ion Transition

The question involves calculating the frequency of light emitted when an electron in a helium ion (He+) transitions from a higher energy orbit to a lower one. Specifically, from n1=2 to n2=1. Using the Bohr model of the atom, this can be understood as the electron dropping from one quantized energy level to another, releasing a photon whose energy corresponds to the difference between these two energy states.

The energy difference (ΔE) between two orbits in a hydrogen-like atom is given by the formula:

ΔE= Z2RH(1/n12 - 1/n22)

Here, Z is the atomic number of helium (Z=2), RH is the Rydberg constant for hydrogen (approximately 13.6 eV), n1 and n2 are the principal quantum numbers of the initial and final orbits, respectively. The frequency (f) of the emitted photon is related to the energy difference by Planck's equation:

E= hf, where h is Planck's constant

Now, rearranging for f and using the values for a helium ion, we get:

f = ΔE/h = Z2RH(1/n12 - 1/n22)/h

By substituting the known values into this equation, we can calculate the frequency of the photon produced when the electron falls from orbit 2 to orbit 1 in a helium ion.

User Forseti
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8.0k points
2 votes

Final answer:

The frequency of light emitted by an electron transitioning from orbit n1=2 to n2=1 in a helium ion is calculated using the energy difference between these states and Planck's constant.

Step-by-step explanation:

To find the frequency of light f radiated by an electron moving from orbit n1=2 to n2=1 inside of a helium ion (He+), we use the Bohr model of the atom. The frequency of the emitted light is directly proportional to the energy difference (ΔE) between these two orbits. The energy difference can be calculated using the formula ΔE = 2μB B, where μ is the magnetic moment and B is the magnetic field strength. Plugging in the given values, we get ΔE = 2(5.79 × 10-5 eV)(1.5T). Using Planck's constant (h), the frequency f is obtained via the formula ΔE/h. With Planck's constant being 4.136 × 10-15 eV·s, we can calculate the frequency of the emitted light.

User Lmgonzalves
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8.6k points
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