Question

What is the wavelength (in meters) of photons with the following energies? In what region of the electromagnetic spectrum does each appear?​

A) 148 kJ/mol

B)4.65×10⁻² kJ/mol

C) 4.76×10⁴ kJ/mol

Answer 1

A)

energy = 148 KJ = 148000 J

1 mole contain 6.022 10²³ molecule hence, 1 photon energy = 1 148000 / 6.022 10²³ = 2.457655 10^-19 J

we know equation

E = hc / where,

E = energy of photon = 2.457655 10^-19 J

h = Planck constant = 6.62610^-34J s

c = velocity of light = 3.0010⁸ m/s

= wavelength in meter = ?

we can wright above equation

= hc/E

Substitute value

= (6.62610^-34)(3.0010⁸) / (2.457655 10^-19)

= 8.0882 10^-7 m

1m = 1 10⁹ nm

then 8.0882 10^-7 m = 808.82 nm

B)

energy  = 4.65 10^-2 KJ = 4650 J

1 mole contain 6.022 10²³ molecule hence, 1 photon  energy = 1 4650 / 6.022 10²³ = 7.721687 10^-21 J

we know equation

E = hc / where,

E = energy of photon = 7.721687 10^-21 J

h = Planck constant = 6.62610^-34J s

c = velocity of light = 3.0010⁸ m/s

= wavelength in meter = ?

we can wright above equation

= hc/E

Substitute value

= (6.62610^-34)(3.0010⁸) / (7.721687 10^-21)

= 2.5743 10^-5 m

1m = 1 10⁹ nm

then 2.5743 10^-5 m = 25743 nm

C)

energy  = 4.76 10⁴ KJ = 47600000 J

1 mole contain 6.022 10²³ molecule hence, 1 photon  energy = 1 47600000 / 6.022 10²³ = 7.90 10^-17 J

we know equation

E = hc / where,

E = energy of photon = 7.90 10^-17 J

h = Planck constant = 6.62610^-34J s

c = velocity of light = 3.0010⁸ m/s

= wavelength in meter = ?

we can wright above equation

= hc/E

Substitute value

= (6.62610^-34)(3.0010⁸) / (7.90 10^-17)

= 2.516 10^-9 m

1m = 1 10⁹ nm

then 2.516 10^-9 m = 2.516 nm