An electron of wavelength 1.74*10-10m strikes an atom of ionized helium (He+). What is the wavelength (m) of the light corresponding to the line in the emission spectrum with the smallest energy transition?

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1.75329*10^-10

Ya that's right

It's not 1.75329*10^-10.

What is it?

1.64*10^-7 m

To find the wavelength of the light corresponding to the line in the emission spectrum with the smallest energy transition, we need to first determine the energy transition involved.

The energy of a photon is given by the equation E = hf, where E is the energy, h is the Planck's constant (6.626 × 10^-34 J·s), and f is the frequency of the light.

Since the electron is striking an atom of ionized helium (He+), we can assume that it is being captured by the ionized helium to form a bound state. This results in the emission of a photon with the energy corresponding to the difference in energy levels between the initial and final state.

The energy of an electron with wavelength λ can be calculated using the equation E = hc/λ, where c is the speed of light (2.998 × 10^8 m/s).

So, to find the wavelength of the emitted light, we need to calculate the difference in energy between the initial and final state and then use that energy to calculate the corresponding wavelength.

Let's assume the initial energy level is E1 and the final energy level is E2.

1. Calculate the energy of the incident electron:
E1 = hc/λ
E1 = (6.626 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (1.74 × 10^-10 m)

2. Calculate the energy of the emitted photon:
E2 = E1 - E

Since we are looking for the smallest energy transition, we assume the final energy level is the ground state of the helium ion (He+) with energy E2 = 0.

E2 = 0

Rearranging the equation, we get:
E = E1

3. Calculate the wavelength of the emitted light:
λ = hc/E
λ = (6.626 × 10^-34 J·s) × (2.998 × 10^8 m/s) / E1

Plug in the initial energy E1 calculated in step 1 to get the final wavelength.

By following these steps, you will be able to find the wavelength of the light corresponding to the line in the emission spectrum with the smallest energy transition.