Question

1) Ionization involves completely removing an electron from an atom. Light of a particular wavelength can cause ionization to occur if it has the required energy.
The energy to ionize a certain element is   530   kJ/mol. What wavelength contains enough energy in a single photon to ionize one atom of this element?
Enter your answer with three significant figures.

2) Suppose that the microwave radiation has a wavelength of 12.4 cm . How many photons are required to heat 255 mL of coffee from 25.0 ∘Cto 62.0 ∘C? Assume that the coffee has the same density, 0.997 g/mL , and specific heat capacity, 4.184 J/(g⋅K) , as water over this temperature range.
Express the number of photons numerically.

3)Which of the following transitions in the hydrogen atom correspond to light being emitted?
n = 2 to n = 3
n = 4 to n = 5
n = 5 to n = 2
n = 3 to n = 1
n = 1 to n = 4

Answer 1

1) E= h x c/

h= 6.626x10^-34 J/s

c= 3x10⁸m/s

= wavelength

Now, we have the energy per mol of substance. So, 1 mol are 6.02x10²³ atoms, that means that 530 kJ of energy can ionize  6.02x10²³ atoms, but the question says "to ionize 1 atom". Then, the energy will be:

E= 530 kJ/mol/6.02x10²³ atoms/mol = 8.8x10^-22 kJ/atom= 8.8x10^-19 J/atom

8.8x10^-19 J =(6.626x10^-34 J/s x 3x10⁸m/s)/

= 2.26x10^-7m = 226 nm (i don´t know the unit that you need to put the answer)

2) Heat needed to increase the temperature of the water:

H= mass x C x DT

H= (255mL x 0.997g/mL) x 4.184 J/g.K x 37K = 39357.6 J

wavelength= 0.124m

E= h x c/

E= 6.626x10^-34 J/s x 3x10⁸ m/s/0.124m = 1.6x10^-24 J

1.6x10^-24 J is the energy emitted by 1 photon, but we need 39357.6 J to heat the water:

photons needed= 39357.6 J x 1photon/1.6x10^-24 J = 2.5x10²⁸ photons

3) When the electron goes from a lower energy level to a higher one, as in n=2 to n=3 the atom needs to absorb energy. But, when the electron falls from a higher energy level to a lower one, as in n=5 to n=2 and n=3 to n=1, it emits energy in the form of light.