Atomic Structure Problems
Problems in Atomic Structure:
What is the ratio between energy of two types of radiation whose wavelengths are 6000 Angstrom and 2000 Angstrom respectively?
Answer:To find the ratio of the energy of two types of radiation based on their wavelengths, we use the following relationship between energy and wavelength:
E = hc / λ
Where:
- E is the energy of the radiation,
- h is Planck's constant (6.626 × 10-34 J·s),
- c is the speed of light (3 × 108 m/s),
- λ is the wavelength of the radiation.
- For the first radiation, λ1 = 6000 Å = 6000 × 10-10 m = 6 × 10-7 m
- For the second radiation, λ2 = 2000 Å = 2000 × 10-10 m = 2 × 10-7 m
The ratio of energy E1 (for λ1) to E2 (for λ2) is given by:
E₁ / E₂ = λ₂ / λ₁
E₁ / E₂ = (2 × 10-7) / (6 × 10-7) = 2 / 6 = 1 / 3
2.What is the ratio between the number of neutrons present in carbon isotopes with mass numbers 12 and 14?
Carbon-12 and Carbon-14 are isotopes of carbon. Isotopes have the same number of protons but different numbers of neutrons. .
- Carbon-12 (C-12): The mass number is 12. The number of neutrons is:
Neutrons = Mass Number - Protons = 12 - 6 = 6 neutrons.
- Carbon-14 (C-14): The mass number is 14. The number of neutrons is:
Neutrons = Mass Number - Protons = 14 - 6 = 8 neutrons.
The ratio of neutrons in Carbon-12 to Carbon-14 is:
Neutrons in C-12 / Neutrons in C-14 = 6 / 8 = 3 / 4
Conclusion:
The ratio between the number of neutrons in Carbon-12 and Carbon-14 is 3:4.
3.What are the number of protons, electrons, and neutrons present in a nitride ion (N³⁻)?
The following table shows the number of protons, electrons, and neutrons present in a nitride ion (N³⁻):
| Particle | Number in Nitride Ion (N³⁻) |
|---|---|
| Protons | 7 |
| Electrons | 10 |
| Neutrons | 7 |
Explanation:
- Protons: The atomic number of nitrogen is 7, so the number of protons is 7.
- Electrons: The nitride ion (N³⁻) has gained 3 extra electrons, so it has 7 + 3 = 10 electrons.
- Neutrons: The most common isotope of nitrogen has a mass number of 14. Neutrons are calculated as mass number - atomic number, so 14 - 7 = 7 neutrons.
