To calculate the wavelength of the peak of the black-body spectrum emitted by the surface of a star, we can use Wien's Displacement Law. The formula for this law is:

λ_max = b / T

where:
- λ_max is the wavelength at which the emission is maximum,
- b is Wien's constant (approximately 2.898 x 10^-3 m.K),
- T is the absolute temperature of the black body (in this case, the surface of the star).

Given that the temperature T of the star is 8200 K, we can substitute this value into the formula:

λ_max = (2.898 x 10^-3 m.K) / 8200 K

Solving this equation gives us the wavelength in meters. To convert this to nanometers (nm), we multiply by 10^9 (since 1 m = 10^9 nm).

Let's calculate:

λ_max = (2.898 x 10^-3 m.K) / 8200 K * 10^9 nm/m

After calculating, we get λ_max ≈ 353.66 nm.

Rounding to the nearest nm, we get λ_max ≈ 354 nm.

Question

To calculate the wavelength of the peak of the black-body spectrum emitted by the surface of a star, we can use Wien's Displacement Law. The formula for this law is:

λ_max = b / T

where:
- λ_max is the wavelength at which the emission is maximum,
- b is Wien's constant (approximately 2.898 x 10^-3 m.K),
- T is the absolute temperature of the black body (in this case, the surface of the star).

Given that the temperature T of the star is 8200 K, we can substitute this value into the formula:

λ_max = (2.898 x 10^-3 m.K) / 8200 K

Solving this equation gives us the wavelength in meters. To convert this to nanometers (nm), we multiply by 10^9 (since 1 m = 10^9 nm).

Let's calculate:

λ_max = (2.898 x 10^-3 m.K) / 8200 K * 10^9 nm/m

After calculating, we get λ_max ≈ 353.66 nm.

Rounding to the nearest nm, we get λ_max ≈ 354 nm.

Knowee AI · Accepted Answer

To calculate the wavelength of the peak of the black-body spectrum emitted by the surface of a star, we can use Wien's Displacement Law. The formula for this law is:

λ_max = b / T

where:
- λ_max is the wavelength at which the emission is maximum,
- b is Wien's constant (approximately 2.898 x 10^-3 m.K),
- T is the absolute temperature of the black body (in this case, the surface of the star).

Given that the temperature T of the star is 8200 K, we can substitute this value into the formula:

λ_max = (2.898 x 10^-3 m.K) / 8200 K

Solving this equation gives us the wavelength in meters. To convert this to nanometers (nm), we multiply by 10^9 (since 1 m = 10^9 nm).

Let's calculate:

λ_max = (2.898 x 10^-3 m.K) / 8200 K * 10^9 nm/m

After calculating, we get λ_max ≈ 353.66 nm.

Rounding to the nearest nm, we get λ_max ≈ 354 nm.

Calculate the wavelength of the peak in nanometres (nm) of the black-body spectrum emitted by the surface of the star at a temperature of 8200 K. Give your answer to the nearest nm.

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