During nuclear fusion, it is observed that when two hydrogen atoms are fused together to form one helium atom, there is a loss in mass, M. The atomic masses of one hydrogen atom and one helium atom are given in the table below. The masses are given in atomic mass unit (u).

  1. (a)

    Find M (in u), leaving your answer in standard form.

    Answer ... u

  2. (b)

    Express M as a percentage of the atomic mass of one helium atom.

    Answer ... %

  3. (c)

    Given that 1 u = 1.6607 = 1.66 x 10^-27 kg, find M in kilograms.

    Answer ... kg

Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

5(a)

1. Find the mass of two hydrogen atoms and subtract the mass of one helium atom.

Mass of two hydrogen atoms:
2×2.0141=4.0282 u2 \times 2.0141 = 4.0282\text{ u}
Mass lost:
M=4.0282−4.0026=0.0256 uM = 4.0282 - 4.0026 = 0.0256\text{ u}

2. Write the mass loss in standard form.

0.0256=2.56×10−20.0256 = 2.56 \times 10^{-2}

Answer

2.56×10−2 u2.56 \times 10^{-2}\text{ u}

5(b)

1. Form the percentage using mass loss as a fraction of the helium atomic mass.

From part (a), M=2.56×10−2=0.0256M=2.56\times 10^{-2}=0.0256 u.

Percentage=Matomic mass of one helium atom×100%\text{Percentage}=\frac{M}{\text{atomic mass of one helium atom}}\times 100\%

=0.02564.0026×100%=\frac{0.0256}{4.0026}\times 100\%

2. Calculate and round the percentage appropriately.

0.02564.0026×100=0.639584…\frac{0.0256}{4.0026}\times 100=0.639584\ldots

≈0.640\approx 0.640

Answer

0.640%0.640\%

5(c)

1. Convert the mass loss from atomic mass units to kilograms.

From part (a),
M=2.56×10−2 u.M=2.56\times 10^{-2}\text{ u}.
Given 1 u=1.66×10−27 kg1\text{ u}=1.66\times 10^{-27}\text{ kg},
M=(2.56×10−2)(1.66×10−27)M=(2.56\times 10^{-2})(1.66\times 10^{-27})
=4.2496×10−29 kg=4.2496\times 10^{-29}\text{ kg}
≈4.25×10−29 kg.\approx 4.25\times 10^{-29}\text{ kg}.

Answer

4.25×10−29 kg4.25\times 10^{-29}\text{ kg}

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

More questions on this topic

  1. 1近似数2.302.30万精确到___位,用科学记数法表示:___.
  2. 2A piece of wood which was 50 cm long, was in the shape of a uniform cylinder. A prism is cut out from the wood such that…
  3. 3中国是严重缺水的国家之一,人均淡水资源为世界人均水平的四分之一,所以我们要节约用水.若每人每天浪费水0.30.3升,则马鞍山全市230230万人每天浪费的水的总升数,用科学记数法表示为()(\quad) A. 6.9×1056.9×10^{5}…
  4. 4Mr Johnson has a plot of field that grows dandelion plants. An average of 70 dandelion plants grow on each square metre.…
  5. 5据报道,发射“天宫一号”的“长征二号”火箭的起飞质量约为493000kg.493000kg.数字493000493000用科学记数法表示为()(\quad) A. 49.3×10449.3×10^{4} B. 493×103493×10^{3} C. 4.93×1054.93×10^{5}…