A tritium nucleus is formed by combining two
neutrons and a proton. The mass of this nucleus
is 9.106 × 10–3 universal mass unit less than the
combined mass of the particles from which it is
formed. Approximately how much energy is
released when this nucleus is formed?
To determine the energy released during the formation of a tritium nucleus, we can use Einstein's mass-energy equivalence principle, which states that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared, using the equation E=mc^2.
First, let's calculate the mass difference between the tritium nucleus and the combined masses of the particles from which it is formed.
Given:
Mass of a proton (mp) = 1.0072766 atomic mass unit (AMU)
Mass of a neutron (mn) = 1.0086654 AMU
The combined mass of the particles from which the tritium nucleus is formed is:
2 neutrons + 1 proton = 2mn + mp
The mass difference is given as:
Δm = (mass of tritium nucleus) - (combined mass of particles)
Δm = 9.106 × 10^(-3) universal mass unit (UMU)
Now, we can convert the mass difference from universal mass units to atomic mass units (AMU) by using the conversion factor: 1 UMU = 1.66053904 × 10^(-27) kg = 1 AMU.
Δm = 9.106 × 10^(-3) AMU
Next, we need to convert the mass difference to kilograms. Multiply the mass difference by the conversion factor: 1 AMU = 1.66053904 × 10^(-27) kg.
Δm = 9.106 × 10^(-3) × (1.66053904 × 10^(-27)) kg
≈ 1.512 × 10^(-29) kg
Now, we can calculate the energy released using the equation: E = Δm × c^2, where c is the speed of light and approximately equals 3.00 × 10^8 m/s.
E = (1.512 × 10^(-29) kg) × (3.00 × 10^8 m/s)^2
≈ 1.357 × 10^(-12) Joules
Therefore, approximately 1.357 × 10^(-12) Joules of energy is released when the tritium nucleus is formed.
To determine the energy released when a tritium nucleus is formed, you can use Einstein's mass-energy equivalence principle (E=mc²), where E is the energy, m is the mass, and c is the speed of light.
First, we need to find the difference in mass between the tritium nucleus and the individual particles (two neutrons and a proton) from which it is formed. The given information states that the tritium nucleus is 9.106 × 10–3 universal mass units (u) less than the combined mass of the particles it contains.
Next, we convert the mass difference from universal mass units to kilograms, as energy is typically measured in joules (J). The conversion factor is 1 u ≈ 1.66 × 10⁻²⁷ kg.
Mass difference = 9.106 × 10–3 u * (1.66 × 10⁻²⁷ kg/u)
Mass difference = 1.511796 × 10⁻²⁹ kg
Now, we can calculate the energy released using the mass-energy equivalence principle:
Energy released = (mass difference) * (speed of light)²
Energy released = 1.511796 × 10⁻²⁹ kg * (3.00 × 10⁸ m/s)²
Now, we just need to calculate this value:
Energy released = 1.511796 × 10⁻²⁹ kg * 9.00 × 10¹⁶ m²/s²
Energy released = 1.3606164 × 10⁻¹² J
Therefore, approximately 1.3606164 × 10⁻¹² joules (J) of energy are released when a tritium nucleus is formed.
E=Δm•c²=
=9.106•10⁻³•1.67•10⁻²⁷•(3•10⁸)²=1.37•10⁻¹²J