What is the energy (in J) of a photon of ultra-violet light that has a wavelength of 252 nm? The units for the answer are Joules. The error interval is 5%.
I did the problem and i got 7.893E-37
did i do correct or was i close
The number is right. The exponent is not.
E = 6.626E-34*3E8/252E-9 = ??
To calculate the energy of a photon, you can use the equation:
Energy (E) = Planck's constant (h) * speed of light (c) / wavelength (λ)
Let's first convert the given wavelength from nanometers (nm) to meters (m):
252 nm = 252 × 10^-9 m
Now, let's plug the values into the equation:
E = (6.62607015 × 10^-34 J·s) * (2.998 × 10^8 m/s) / (252 × 10^-9 m)
E ≈ 2.484 × 10^-19 J
Based on your calculation, you obtained 7.893 × 10^-37 J, which is significantly different from the correct answer of 2.484 × 10^-19 J.
Let's calculate the percent error to determine how close your answer was to the correct one:
Percent Error = |Correct Value - Your Value| / Correct Value * 100
Percent Error = |2.484 × 10^-19 J - 7.893 × 10^-37 J| / 2.484 × 10^-19 J * 100
Percent Error ≈ 99.9968%
Therefore, your answer is not close to the correct value and there seems to be an error in your calculation.
To determine the energy of a photon of ultraviolet light, you can use the equation:
E = (hc) / λ
Where:
E is the energy of the photon,
h is Planck's constant = 6.62607015 × 10^-34 J·s,
c is the speed of light = 2.998 × 10^8 m/s,
and λ is the wavelength of the light in meters.
First, convert the given wavelength from nanometers to meters:
252 nm = 252 × 10^-9 m = 2.52 × 10^-7 m.
Now, substitute this value into the equation:
E = (6.62607015 × 10^-34 J·s × 2.998 × 10^8 m/s) / (2.52 × 10^-7 m)
E ≈ 9.92280139 × 10^-19 J
To check if your answer is correct within the given error interval:
Lower bound: 9.92280139 × 10^-19 J - 5% = 9.426661326 × 10^-19 J
Upper bound: 9.92280139 × 10^-19 J + 5% = 1.041394945 × 10^-18 J
Comparing your answer of 7.893E-37 J to the error interval:
9.426661326 × 10^-19 J < 7.893E-37 J < 1.041394945 × 10^-18 J
Your answer is much smaller than the lower bound of the error interval, indicating that there may have been an error in your calculation. Please recheck your calculations, making sure to use the correct values for Planck's constant, the speed of light, and the wavelength, and perform the division accurately to get the correct answer.