An electron releases energy as it moves from the 6^th shell to the 3^rd shell. If it releases 4.25 x 10⁹ kJ of energy at a wavelength of 915.7 nm, how many photons were released in the process?

• A. 8.96 x 10³¹ photons
• B. 1.96 x 10³¹ photons
• C. 1.82 x 10²⁹ photons
• D. 2.98 x 10³¹ photons

Answer: (B)

Verified step by step guidance

1. Understand that the energy released by an electron moving between shells is related to the energy of the photons emitted. The energy of a photon can be calculated using the formula: E = \( \frac{hc}{\lambda} \), where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and \( \lambda \) is the wavelength.
2. Convert the given wavelength from nanometers to meters for consistency in units. Since 1 nm = 1 x 10^-9 m, convert 915.7 nm to meters.
3. Calculate the energy of a single photon using the formula E = \( \frac{hc}{\lambda} \). Substitute the values for h, c, and the converted wavelength into the equation to find the energy of one photon.
4. Determine the total energy released by the electron transition, which is given as 4.25 x 10^9 kJ. Convert this energy into joules by multiplying by 1,000 (since 1 kJ = 1,000 J).
5. Calculate the number of photons released by dividing the total energy released (in joules) by the energy of a single photon (also in joules). This will give you the number of photons emitted during the transition.