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Figure 1 shows nuclear notation and schematic emission and absorption spectra for an element.
In the nuclear notation shown in Figure 1, state what and represent, and calculate the number of neutrons in the nucleus.
Describe one feature of the line positions in the spectra shown in Figure 1.
Explain how the spectra provide evidence that atomic energy levels are discrete.
Figure 1 shows four nuclear transformations. In the first sequence, the nucleus formed after alpha decay becomes the parent nucleus in the following beta-minus decay. The symbol * denotes an excited nucleus.
Write the complete nuclear equation for the alpha decay in the first sequence.
Using your answer to (a), write the complete nuclear equation for the beta-minus decay in the first sequence. Include all emitted particles.
Write the complete nuclear equation for the beta-plus decay shown in Figure 1. Include all emitted particles.
Write the complete nuclear equation for the gamma emission shown in Figure 1.
One possible neutron-induced fission reaction of uranium-235 is
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n
The following rest masses are available:
| Particle or atom | Rest mass / u |
|---|---|
| ²³⁵U | 235.043930 |
| ¹n | 1.008665 |
| ¹⁴¹Ba | 140.914411 |
| ⁹²Kr | 91.926156 |
Distinguish between spontaneous fission and neutron-induced fission.
For the reaction and data above, use 1 u c² = 931.5 MeV and 1 MeV = 1.60 × 10⁻¹³ J.
Determine the energy released in the reaction, in MeV.
Using your answer to (b)(i), express the energy released in joules.
Explain how neutrons released in fission can sustain a chain reaction in uranium-235.
In the core of a young star, deuterium nuclei fuse with protons according to
Figure 1 shows the binding energy per nucleon for the nuclei relevant to this reaction. The plotted values are approximate.
Use
Use Figure 1 to determine the energy released per reaction. Give your answer in MeV to two significant figures.
At a particular stage, this reaction occurs at a rate of Calculate the energy released per second by these reactions. Give your answer in W to two significant figures.
The reaction rate then falls to half its value in (b), while the energy released per reaction remains unchanged. Determine the new energy released per second and explain how it compares with your answer to (b).
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