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An element of mass M has Z protons and N...

An element of mass M has Z protons and Nneutrons. Masses of proton and neutron are `m_(p) and m_(n)` respectively. Choose the correct relation among following options.

A

`M gt Zm_(p)+Nm_(n)`

B

`M=Zm_(p)+Mn_(n)`

C

`M lt Zm_(p)+Nm_(n)`

D

M may be greater than, less than or equal to `Zm_(p)+Nm_(n)` depending on natures

Text Solution

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The correct Answer is:
To solve the question regarding the mass of an element with Z protons and N neutrons, we need to derive the correct relation among the given options. ### Step-by-Step Solution: 1. **Understanding the Mass of the Element**: The mass of the element can be calculated based on the number of protons and neutrons it contains. The total mass (M) of the element is given by the sum of the masses of its protons and neutrons. 2. **Writing the Mass Equation**: The mass of the element can be expressed as: \[ M = Z \cdot m_p + N \cdot m_n \] where: - \( M \) is the total mass of the element, - \( Z \) is the number of protons, - \( N \) is the number of neutrons, - \( m_p \) is the mass of a proton, - \( m_n \) is the mass of a neutron. 3. **Identifying the Correct Relation**: The equation \( M = Z \cdot m_p + N \cdot m_n \) represents the total mass of the element in terms of the number of protons and neutrons and their respective masses. This is the fundamental relation we need to analyze. 4. **Conclusion**: The correct relation among the options provided is: \[ M = Z m_p + N m_n \]
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