Calculating the Mass Defect of 40Ca

In summary, the mass defect of 40Ca is the difference between the actual mass of a 40Ca atom and the sum of the masses of its individual protons and neutrons. It is calculated using the formula Δm = Zm<sub>p</sub> + Nm<sub>n</sub> - m<sub>atom</sub>. This calculation is significant because it helps us understand the binding energy of atomic nuclei, which plays a crucial role in nuclear reactions and stability of atoms. The mass defect is also directly related to nuclear binding energy, and can be measured experimentally using mass spectrometry. By understanding the mass defect of 40Ca, we can better understand and predict the energy released or absorbed in nuclear reactions
  • #1
Intrusionv2
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Homework Statement



What is the mass defect of the 40Ca nucleus?

Homework Equations



Δm=(Zmp+(A-Z)mn)-m

The Attempt at a Solution



mass of 40Ca=40.078 amu
mass of proton in amu is mp=1.0073 amu
mass of neutron is mn=1.0087 amu
atmomic number of 40Ca is Z=20
its mass number is A=40
so the mass defect is
Δm=(Zmp+(A-Z)mn)-m
=0.242 amu

But it says the correct answer is 0.367u, why? What am I doing wrong? Thanks.
 
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  • #2
Δm=(Zmp+(A-Z)mn)-(m-Zme)
Now the formula looks better :)
 
  • #3
Nvm, got it, thanks
 
Last edited:

Related to Calculating the Mass Defect of 40Ca

1. What is the mass defect of 40Ca and how is it calculated?

The mass defect of 40Ca is the difference between the actual mass of a 40Ca atom and the sum of the masses of its individual protons and neutrons. It is calculated using the formula Δm = Zmp + Nmn - matom, where Z is the number of protons, N is the number of neutrons, mp and mn are the masses of a proton and neutron respectively, and matom is the actual mass of the 40Ca atom.

2. What is the significance of calculating the mass defect of 40Ca?

Calculating the mass defect of 40Ca is significant because it allows us to better understand the binding energy of atomic nuclei. The difference between the actual mass and the sum of the individual masses represents the amount of energy that is released when the nucleus is formed. This energy is known as binding energy and it plays a crucial role in nuclear reactions and stability of atoms.

3. How is the mass defect of 40Ca related to nuclear binding energy?

The mass defect of 40Ca is directly related to nuclear binding energy. As mentioned before, the difference between the actual mass and the sum of the individual masses represents the binding energy of the nucleus. This energy is responsible for holding the protons and neutrons together in the nucleus, and the stronger the binding energy, the more stable the nucleus is.

4. Can the mass defect of 40Ca be measured experimentally?

Yes, the mass defect of 40Ca can be measured experimentally using mass spectrometry. Mass spectrometry is a technique that can accurately measure the mass of atoms and molecules. By comparing the actual mass of 40Ca atoms to the calculated mass using the formula, the mass defect can be determined.

5. How does the mass defect of 40Ca contribute to our understanding of nuclear reactions?

The mass defect of 40Ca plays a crucial role in understanding nuclear reactions. In nuclear reactions, atoms undergo changes in their nuclei, resulting in a release or absorption of energy. By knowing the mass defect of 40Ca, we can predict the amount of energy that will be released or absorbed in a nuclear reaction, providing valuable insights into the process and potential applications of nuclear energy.

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