Question

question 5.3.9
a line in a bright line spectra of mercury is observed using a hand - held spectroscope and assigned a scale value of unclear. determine:
a. the wavelength of this light
enter the value in nm to the nearest 5 nm.
do not enter the unit. 495 nm
b. the energy of a photon with this wavelength
enter the value in j/photon using e - format for scientific notation and four digits (1.234×10⁻⁵ = 1.234e - 5)
do not enter the unit. 4.010e - 19 j/photon
c. the energy of a mole of these photons
enter the value in kj/mol to the nearest 0.1 kj/mol.
do not enter the unit. 241.5 kj/mol

Explanation:

Step1: Recall the conversion factor for wavelength

1 nm = 10^{-9} m. Given wavelength \(\lambda = 495\ nm=495\times10^{-9}\ m\)

Step2: Use the energy - wavelength formula for a single photon

The energy of a photon is given by \(E = h
u=\frac{hc}{\lambda}\), where \(h = 6.626\times10^{-34}\ J\cdot s\) and \(c = 3\times10^{8}\ m/s\).
\[E=\frac{6.626\times 10^{-34}\ J\cdot s\times3\times 10^{8}\ m/s}{495\times 10^{-9}\ m}=4.010\times 10^{-19}\ J/photon\]

Step3: Calculate the energy of a mole of photons

1 mole of photons contains \(N_A = 6.022\times10^{23}\) photons. The energy of a mole of photons \(E_{mol}=N_A\times E\).
\[E_{mol}=6.022\times 10^{23}\times4.010\times 10^{-19}\ J/mol = 2.415\times10^{5}\ J/mol\]
Convert to kJ/mol: \(E_{mol}=\frac{2.415\times 10^{5}\ J/mol}{1000\ J/kJ}=241.5\ kJ/mol\)

Answer:

a. 495
b. 4.010E - 19
c. 241.5