Calculate the energy in kJ/mol of light with a wavelength of 450 nm.  (h: 6,626×10-34Js; c: 3x108ms-1; NA: 6,02×1023 mol-1)
ÂÂ
 A
4.42×10-19 kJ/mol
B ÂÂ
266 kJ/mol      ÂÂ
C ÂÂ
6.63×103 kJ/mol
D ÂÂ
4.42×10-22 kJ/mol   ÂÂ
E ÂÂ
0.266 kJ/mol
The Correct Answer and Explanation is :
To calculate the energy of light in kJ/mol, we can use the following formula:
[
E = \dfrac{hc}{\lambda}
]
Where:
- (E) is the energy of one photon (in joules),
- (h) is Planck’s constant ((6.626 \times 10^{-34}) J·s),
- (c) is the speed of light ((3.0 \times 10^8) m/s),
- (\lambda) is the wavelength of the light (in meters).
Step 1: Convert the wavelength to meters.
Given that the wavelength is 450 nm (nanometers), we convert it to meters:
[
450 \, \text{nm} = 450 \times 10^{-9} \, \text{m}
]
Step 2: Calculate the energy per photon in joules.
Substitute the known values into the equation:
[
E = \dfrac{(6.626 \times 10^{-34} \, \text{J·s}) \times (3.0 \times 10^8 \, \text{m/s})}{450 \times 10^{-9} \, \text{m}}
]
[
E = \dfrac{1.9878 \times 10^{-25}}{450 \times 10^{-9}} = 4.42 \times 10^{-19} \, \text{J}
]
Step 3: Convert energy per photon to energy per mole.
To find the energy per mole, multiply by Avogadro’s number ((N_A = 6.02 \times 10^{23} \, \text{mol}^{-1})):
[
E_{\text{mol}} = (4.42 \times 10^{-19} \, \text{J}) \times (6.02 \times 10^{23} \, \text{mol}^{-1})
]
[
E_{\text{mol}} = 2.66 \times 10^5 \, \text{J/mol}
]
Step 4: Convert to kJ/mol.
Since 1 kJ = 1000 J:
[
E_{\text{mol}} = \dfrac{2.66 \times 10^5 \, \text{J/mol}}{1000} = 266 \, \text{kJ/mol}
]
Final Answer:
The correct answer is B) 266 kJ/mol.
Explanation:
This process demonstrates how to calculate the energy of light using the energy formula for photons. First, the wavelength is converted to meters. Next, the energy of a single photon is calculated using the constants of Planck’s constant and the speed of light. Finally, the energy is converted from joules per photon to joules per mole by multiplying with Avogadro’s number. The conversion to kJ/mol gives the energy in more convenient units for chemistry applications.