A typical human eye will respond to wavelengths from about 390 to 750 nm

Answer:

Upper energy = 306.94 kJ/mol ( 390 nm), and lower energy = 159.61 kJ/mol ( 750 nm)

Calculation :

For 390 nm :

1) Convert nm to m:

390.0 nm = 390.0 x 10¯⁹ m = 3.90 x 10¯⁷ m

2) Determine the frequency:

λν = c

(3.90 x 10¯⁷ m) (x) = 3.00 x 10⁸ m/s

x = 7.69 x 10¹⁴ s¯¹

3) Determine the energy:

E = hν:

x = (6.626 x 10¯³⁴ J s) (7.69 x 10¹⁴ s¯¹)

x = 5.10 x 10¯¹⁹ J

Important point: this is the energy for one photon.

4) Determine energy for one mole of photons:

(3.9756 x 10¯¹⁹ J) (6.022 x 10²³ mol¯¹)

306.94 kJ/mol

For 750 nm :

1) Convert nm to m:

750.0 nm = 750.0 x 10¯⁹ m = 7.50 x 10¯⁷ m

2) Determine the frequency:

λν = c

(7.50 x 10¯⁷ m) (x) = 3.00 x 10⁸ m/s

x = 4.00 x 10¹⁴ s¯¹

3) Determine the energy:

E = hν:

x = (6.626 x 10¯³⁴ J s) (4.00 x 10¹⁴ s¯¹)

x = 2.65 x 10¯¹⁹ J

Important point: this is the energy for one photon.

4) Determine energy for one mole of photons:

(2.65 x 10¯¹⁹ J) (6.022 x 10²³ mol¯¹)

159.61 kJ/mol