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 6.80. 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 - 10 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: Find wavelength from scale - value relationship (assumed known conversion)

Wavelength $\lambda = 495$ nm (given in part a answer)

Step2: Calculate energy of a single photon

Use the formula $E = \frac{hc}{\lambda}$, where $h = 6.626\times10^{-34}$ J s (Planck's constant), $c = 3.0\times10^{8}$ m/s (speed of light), and $\lambda = 495\times10^{-9}$ m.
$E=\frac{6.626\times10^{-34}\times3.0\times10^{8}}{495\times10^{-9}}=4.010\times10^{-19}$ J/photon (in scientific - notation $4.010E - 19$ J/photon)

Step3: Calculate energy of a mole of photons

Use Avogadro's number $N_A=6.022\times10^{23}$ photons/mol.
$E_{mol}=E\times N_A=4.010\times10^{-19}\times6.022\times10^{23}=2.415\times10^{5}$ J/mol. Convert to kJ/mol: $E_{mol}=241.5$ kJ/mol.

Answer:

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