this is KCET question...

The atomic mass of C-12 is 12.0032. Find the mass defect.

a) 0.03 b) 0.0034 c) 0.034 c) none

The answer is 0.0034

Howz that possible ...

isn't mass defect for a nucleus _ZX^{A - Z} having atomic no. Z and mass no. A

= Zm_p+ (A - Z)m_n - m( _ZX^{A - Z} ) ???

But what is used here seems as if mass defect = M - A

where M is actual mass and the mass number A (not even a mass).

Please explain this concept to me .... from where did this weird formula of difference of a mass and a number came for mass defect ??

Let's break down the concept of mass defect and clarify how it relates to the atomic mass of an isotope like Carbon-12 (C-12). The mass defect is a crucial concept in nuclear physics that helps us understand the stability of atomic nuclei. It arises from the difference between the mass of a nucleus and the sum of the individual masses of its constituent protons and neutrons.

Understanding Mass Defect

The mass defect can be calculated using the formula:

• Mass Defect (Δm) = (Z × m_p + (A - Z) × m_n) - m_nucleus

Here:

• Z is the atomic number (number of protons).
• A is the mass number (total number of protons and neutrons).
• m_p is the mass of a proton (approximately 1.0073 u).
• m_n is the mass of a neutron (approximately 1.0087 u).
• m_nucleus is the actual mass of the nucleus.

Applying the Formula to C-12

For Carbon-12, we have:

• Z = 6 (6 protons)
• A = 12 (6 protons + 6 neutrons)

Using the approximate masses:

• m_p ≈ 1.0073 u
• m_n ≈ 1.0087 u

Now, we can calculate the total mass of the protons and neutrons:

• Total mass of protons = 6 × 1.0073 u = 6.0438 u
• Total mass of neutrons = 6 × 1.0087 u = 6.0522 u
• Total mass = 6.0438 u + 6.0522 u = 12.0960 u

Now, we can find the mass defect:

• Mass defect (Δm) = Total mass of protons and neutrons - Actual mass of nucleus
• Δm = 12.0960 u - 12.0032 u = 0.0928 u

Clarifying the Confusion

Now, regarding your confusion about the formula you mentioned, it seems there was a misunderstanding. The mass defect is indeed calculated using the actual mass of the nucleus and the sum of the masses of the protons and neutrons, not just a simple difference between a mass and a number. The formula you referred to, where it seems like mass defect equals mass minus a number, might have been a misinterpretation.

In the context of your question, the answer of 0.0034 u likely comes from a more precise calculation or a specific context in which the mass defect is being compared to a different standard or reference. It's essential to ensure that the units and values used are consistent and accurate.

Conclusion

In summary, the mass defect is a fundamental concept that illustrates how binding energy affects the stability of a nucleus. The formula you encountered is indeed valid, but it requires careful application of the correct values and understanding of the components involved. If you have any further questions or need clarification on specific points, feel free to ask!

Approved