Question

Halogen lightbulbs allow their filaments to operate at a higher temperature than the filaments in standard incandescent bulbs. For comparison, the filament in a standard lightbulb operates at about 2900K, whereas the filament in a halogen bulb may operate at 3400K. Which bulb has the higher peak frequency? Calculate the ratio of the peak frequencies. The human eye is most sensitive to a frequency around 5.5x10^14 Hz. Which bulb produces a peak frequency close to this value?

Answer 1

Halogen

0.85294

Step-by-step explanation:

c = Speed of light =
`3* 10^8\ m/s`

b = Wien's displacement constant =
`2.897* 10^(-3)\ mK`

T = Temperature

From Wien's law we have

`\lambda_m=(b)/(T)\\\Rightarrow \lambda_m=(2.897* 10^(-3))/(2900)\\\Rightarrow \lambda_m=9.98966* 10^(-7)\ m`

Frequency is given by

`\\u=(c)/(\lambda_m)\\\Rightarrow \\u=(3* 10^8)/(9.98966* 10^(-7))\\\Rightarrow \\u=3.00311* 10^(14)\ Hz`

For Halogen

`\lambda_m=(b)/(T)\\\Rightarrow \lambda_m=(2.897* 10^(-3))/(3400)\\\Rightarrow \lambda_m=8.52059* 10^(-7)\ m`

Frequency is given by

`\\u=(c)/(\lambda_m)\\\Rightarrow \\u=(3* 10^8)/(8.52059* 10^(-7))\\\Rightarrow \\u=3.52088* 10^(14)\ Hz`

The maximum frequency is produced by Halogen bulbs which is closest to the value of
`5.5* 10^(14)\ Hz`

Ratio

`(3.00311* 10^(14))/(3.52088* 10^(14))=0.85294`

The ratio of Incandescent to halogen peak frequency is 0.85294