Question

Calcium \[\left( {Ca} \right)\] has atomic number 20 and mass number 40. Which of the following statements is not correct about \[Ca\] atoms?
a. The number of protons is the same as the number of neutrons.
b. The number of electrons is the same as the number of neutrons.
c. The number of protons is half the number of neutrons.
d. The number of nucleons is double the number of neutrons.

Answer 1

Hint:Here we will first find the number of protons and electrons and nucleons and neutrons and then by seeing their values we will be able to do option verification to get the required answer of the given question.

Complete step by step answer:We know that the element Calcium \[\left( {Ca} \right)\] has atomic number \[\left( Z \right)\] is 20 and mass number \[\left( A \right)\] is 40. So, the Calcium atom is represented as \[{}^{40}C{a_{20{}^{^{}}}}\].
In general, in any atom the atomic number \[\left( Z \right)\] is equal to the number of protons \[\left( P \right)\] of the atom.
\[\therefore \] The atomic number \[\left( Z \right)\] of the Calcium atom \[{}^{40}C{a_{20{}^{^{}}}}\]= Number of protons \[\left( P \right)\] of the Calcium atom \[{}^{40}C{a_{20{}^{^{}}}}\]=20
\[\therefore \] The number of protons\[\left( P \right)\] in calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\] are 20 ………………………….\[\left( 1 \right)\]
We also know that mass of the atom is majorly contributed by nucleus which consists of nucleons (protons + neutrons). Therefore, the mass number \[\left( A \right)\] is equal to the sum of the number of protons \[\left( P \right)\] and number of neutrons \[\left( N \right)\].
Then, mass number \[\left( A \right)\]=number of protons \[\left( P \right)\]+ number of neutrons\[\left( N \right)\]
\[ \Rightarrow A = P + N\]
\[
   \Rightarrow 40 = 20 + N \\
   \Rightarrow 40 - 20 = N \\
   \Rightarrow 20 = N \\
   \Rightarrow N = 20 \\
 \]
\[\therefore \]The number of neutrons \[\left( N \right)\] in calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\] are 20 ………………\[\left( 2 \right)\]
In general, for a neutral atom the number of protons \[\left( P \right)\] of the atom is equal to the number of electrons \[\left( e \right)\] of that atom.
\[\therefore \] The number of protons\[\left( P \right)\] in calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\] =The number of electrons \[\left( e \right)\] in the calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\].
\[ \Rightarrow P = e = 20\]
\[\therefore \]The number of electrons\[\left( e \right)\] in calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\]are 20 ………………\[\left( 3 \right)\]
We already stated that the number of nucleons is equal to the sum of the number of protons\[\left( P \right)\] and the number of neutrons\[\left( N \right)\].
The number of nucleons \[ = P + N\]
\[ \Rightarrow \] The number of nucleons \[ = 20 + 20 = 40\]
\[\therefore \]The number of nucleons in calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\] are 40 ………………\[\left( 4 \right)\]
From \[\left( 1 \right)\] and\[\left( 2 \right)\],
The number of protons \[\left( P \right)\] in calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\] is equal to the number of electrons \[\left( e \right)\] in calcium atom \[{}^{40}C{a_{20{}^{^{}}}}\] .
From \[\left( 2 \right)\] and \[\left( 3 \right)\],
 The number of electrons \[\left( e \right)\] in calcium atom \[{}^{40}C{a_{20{}^{^{}}}}\] is equal to the number of neutrons \[\left( N \right)\] in calcium atom \[{}^{40}C{a_{20{}^{^{}}}}\]
From \[\left( 2 \right)\] and \[\left( 4 \right)\],
The number of protons \[\left( P \right)\] in calcium atom\[{}^{40}C{a_{20{}^{^{}}}}\] is equal to the number of neutrons \[\left( N \right)\] in calcium atom \[{}^{40}C{a_{20{}^{^{}}}}\]
c. The number of protons is half the number of neutrons is the required option.
From \[\left( 2 \right)\] and \[\left( 4 \right)\],
The number of nucleons in calcium atom \[{}^{40}C{a_{20{}^{^{}}}}\] is double to the number of neutrons \[\left( N \right)\] in calcium atom.

Hence, the correct answer is option C.


Note: In general, in any atom the atomic number \[\left( Z \right)\] is equal to the number of protons \[\left( P \right)\] of the atom. The mass of the atom is majorly contributed by nucleus which consists of nucleons (protons + neutrons). In general, for a neutral atom the number of protons \[\left( P \right)\] of the atom is equal to the number of electrons \[\left( e \right)\] of that atom.