# Is this equation for mass defect correct?

I just want to know if this equation for the mass defect is correct

$$\Delta m = Z * m_p + Z * m_e + N* m_n - A$$

where

• Z- Atomic number
• A- Mass number
• N- number of neutrons
• $$m_p$$- mass of the proton
• $$m_n$$- mass of the neutron
• $$m_e$$- mass of the electron

I came up with another formula also $$ΔM=[(Z(m_p)+N(m_n))−(M)]$$ where $$m$$ is the observed mass

Which one is correct and what is the difference between both these equations?

• Possible duplicate of correct formula for Mass Defect / Binding Energy? – Anubhav Srivastava- WASAYANSI Jan 14 at 11:41
• @Peaceman both are correct. – Karthik V Jan 14 at 12:09
• @AnubhavSrivastava-WASAYANSI The answer to your question depends on how (M) is defined. Please tell us what (M) means. Observed mass of what? – Farcher Jan 14 at 12:34
• The first equation doesn't make sense in terms of units. The $-A$ term is unitless. BTW, please make more of an effort to use standard mathematical notation. The *'s and excessive parens make this a chore for other people to decode. – Ben Crowell Jan 14 at 14:19

$$\Delta m = Z * m_p + Z * m_e + N* m_n - A$$
$$A =$$ mass number
A is the mass of an $$^A_Z X$$ atom.
I came up with another formula also $$ΔM=[(Z(m_p)+N(m_n))−(M)]$$ where m is the observed mass.
This is correct if $$(M)$$ is the mass of an $$^A_Z X$$ nucleus.