In a certain 25-W mercury-vapor ultraviolet lamp, 0.1% of the electric energy input
appears as UV radiation of wavelength 2537 AËš . What is the UV photon emission
rate per second from this lamp?
To calculate the UV photon emission rate per second from the lamp, we need to use the given information.
Step 1: Calculate the electric energy input in watts:
The lamp has a power rating of 25 watts.
Step 2: Convert the percentage of electric energy appearing as UV radiation to decimal form:
0.1% is equal to 0.001 (0.1/100).
Step 3: Calculate the electric energy converted to UV radiation:
UV energy emitted = Electric energy input * Percentage of energy converted to UV
UV energy emitted = 25 watts * 0.001
UV energy emitted = 0.025 watts (or 25 milliwatts)
Step 4: Calculate the UV energy per photon:
The energy of a single photon can be calculated using the equation:
E = hc/λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength in meters.
First, convert the wavelength from Angstroms (Å) to meters:
2537 AÅ = 2537 x 10^-10 m
Now, use the equation to calculate the energy per photon:
E = (6.626 x 10^-34 J.s * 3 x 10^8 m/s) / (2537 x 10^-10 m)
E ≈ 2.47 x 10^-19 J
Step 5: Calculate the UV photon emission rate per second:
The photon emission rate can be determined using the equation:
Photon emission rate = UV energy emitted / Energy per photon
Photon emission rate = 0.025 watts / (2.47 x 10^-19 J)
Photon emission rate ≈ 1.01 x 10^17 photons/second
Therefore, the UV photon emission rate per second from this lamp is approximately 1.01 x 10^17 photons/second.