DP Physics (last assessment 2024)

Question 19N.3.HL.TZ0.5

[Maximum mark: 6]

19N.3.HL.TZ0.5

A Σ⁺ particle decays from rest into a neutron and another particle X according to the reaction

Σ⁺ → n + X

The following data are available.

Rest mass of Σ⁺ = 1190 MeV c^–2
Momentum of neutron = 185 MeV c^–1

Calculate, for the neutron,

(a(i))

the total energy.

[1]

Markscheme

neutron energy $= \sqrt{185^{2} + 940^{2}} = 958$ «MeV» ✔

NOTE: Allow 1.5 × 10^–10 «J»

(a(ii))

the speed.

[2]

Markscheme

ALTERNATIVE 1

«use of $E = γ E_{0}$ »

« $958 = 940 γ$ so» $γ = 1.019$ ✔

v = 0.193c ✔

ALTERNATIVE 2

«use of $p = γ m v$ »

$185 = 940 \frac{\frac{v}{c}}{\sqrt{1 - {(\frac{v}{c})}^{2}}}$ ✔

v = 0.193c ✔

ALTERNATIVE 3

«use of $p = γ m v$ »

$v = \frac{p c}{E}$ ✔

$v = \frac{185}{958} = 0.193 c$ ✔

NOTE: Allow v = 5.8 × 10⁷«ms^–1»

(b)

Determine the rest mass of X.

[3]

Markscheme

momentum of X = 185 «MeV c^–1»✔

energy of X = 1190 – 958 = 232 «MeV»✔

$m_{0} = « \sqrt{232^{2} - 185^{2}} = » 140$ «MeV c^–2» ✔

NOTE: Allow mass in kg - gives 2.5 × 10^–28«kg»

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