Question

Part A

Find the frequency of light f radiated by an electron moving from orbit n1=2 to n2=1 inside of a He+ ion.
Express your answer in hertz to three significant figures.
Part B
In the Bohr model of hydrogen, the radius of the nth orbit is defined as
rn=a0n2Z,
where
a0=4???2mee2=5.29

Answer 1

To calculate the frequency of light emitted in a He+ ion electron transition, one must use the Bohr model equations to determine the energy difference for the transition and then use the relation between energy and frequency (ΔE = hf) to find the frequency in Hertz.

Step-by-step explanation:

Calculating the Frequency of Light Emitted by an Electron Transition in He+ Ion

The student's question deals with the Bohr model of the hydrogen-like ion, He+. In Part A, the frequency of light (f) emitted when an electron transitions from a higher orbit (n1) to a lower orbit (n2) is sought. According to Bohr's model, the energy difference between two orbits (ΔE) is related to the frequency (f) of the emitted light by the equation ΔE = hf, where h is Planck's constant. The energy levels for hydrogen-like ions can be represented as En = -Z2R∞/n2, where Z is the atomic number and R∞ is the Rydberg constant for infinite mass.

For a He+ ion (Z=2) and a transition from n1=2 to n2=1, the energy change is ΔE = E2 - E1. By substituting the appropriate energy level expressions, we can calculate the energy difference. The frequency can then be found by rearranging the equation to f = ΔE/h. Remember that the value of f must be expressed in hertz (Hz) for frequency.

For Part B of the question, which Your tutor has not provided instructions for, the same approach can be applied for calculating the energy in joules of a photon emitted during an electron's transition within a different ion.

Answer 2

To find the frequency of light emitted by a He+ ion, calculate the energy difference of orbits using the Bohr model's energy equation and solve for frequency using Planck's equation. For the orbital radius of a hydrogen atom's electron at n=8, use the radius formula with the Bohr radius and atomic number.

Step-by-step explanation:

The question requires the application of the Bohr model to determine the frequency of light emitted by an electron transitioning between orbits within a helium ion (He+). For part A, using the energy levels equation E = -R(Z^2/n^2), where R is the Rydberg constant for helium, Z is the atomic number (2 for helium), and n is the principal quantum number, we can calculate the energy difference (ΔE) between the orbits n1=2 and n2=1. Then, using Planck's equation E = hf, where h is Planck's constant and f is the frequency, we can solve for the frequency of the emitted photon: f = ΔE/h. The steps to calculate the frequency are as follows:

• Calculate the energy of the electron in both orbitals using the energy levels equation.
• Find the energy difference by subtracting the energy of the lower orbit from the higher orbit.
• Divide the energy difference by Planck's constant to find the frequency.

For part B, determining the radius of an electron orbit in a hydrogen atom with n=8 involves using the given radius formula rn = a0n^2/Z. Here, a0 is the Bohr radius, n is the principal quantum number (8), and Z is the atomic number (1 for hydrogen). The radius can be found simply by squaring the principal quantum number, multiplying by the Bohr radius, and dividing by the atomic number.