One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (c) How many photons are in a 1.00 mJ burst of this radiation?

검증된 단계별 안내

Convert the energy of the burst from millijoules to joules. Remember that 1 mJ = 0.001 J.

Calculate the energy of a single photon using the formula: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (6.626 \(\times\) 10^{-34} \(\text{ J s}\)), \( c \) is the speed of light (3.00 \(\times\) 10^8 \(\text{ m/s}\)), and \( \lambda \) is the wavelength in meters (325 nm = 325 \(\times\) 10^{-9} \(\text{ m}\)).

Determine the number of photons by dividing the total energy of the burst by the energy of a single photon: \( \text{Number of photons} = \frac{\text{Total energy}}{\text{Energy per photon}} \).

Ensure all units are consistent, particularly energy in joules and wavelength in meters, to maintain dimensional accuracy.

Perform the division to find the number of photons, ensuring to keep track of significant figures based on the given data.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Photon Energy

The energy of a photon is determined by its wavelength and can be calculated using the equation E = hc/λ, where E is 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 λ is the wavelength in meters. For UV light at 325 nm, this relationship allows us to find the energy of a single photon.

Conversion of Units

In chemistry, it is essential to convert units appropriately to ensure consistency in calculations. In this case, the energy burst of 1.00 mJ must be converted to joules (1 mJ = 0.001 J) to match the units used in the photon energy equation. This step is crucial for accurately determining the number of photons in the given energy burst.

Calculating Number of Photons

To find the number of photons in a given energy burst, divide the total energy by the energy of a single photon. This is expressed mathematically as N = E_total / E_photon, where N is the number of photons, E_total is the total energy in joules, and E_photon is the energy of one photon calculated from its wavelength. This calculation provides insight into the quantized nature of light.