Question

If N = N_2 - N_1 / Z_2 - Z_1 , where N_1 and N_2 are the number of particles per unit Volume at Z_1 and Z_2 respectively . What is the dimensional formula of D ? ​

Answer 1

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$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Correct Question :- }}}}$

❒ The number of particles crossing per unit area perpendicular to z axis per unit time is given by , N = -D ( N₂ - N₁) / ( Z₂ - Z₁ ) , where N₁ and N₂ are the number of particles per unit Volume at Z₁ and Z₂ respectively . What is the dimensional formula of D ?

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Need to FinD :-

• The dimensional formula of D .

$\red{\frak{Given}}\begin{cases}\sf N =-D \dfrac{N_2-N_1}{Z_2-Z_1} \end{cases}$

And N₁ and N₂ ate the number of particles per unit Volume at Z₁ and Z₂ respectively .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ According to Question :- }}}}$

$\sf\dashrightarrow N = -D\dfrac{ N_2-N_1}{Z_2-Z_1} \\\\\\\sf\dashrightarrow D = -N \dfrac{Z_2-Z_1}{N_2-N_1} \\\\\\\sf\dashrightarrow D = \dfrac{ number}{Area*Time} \times \dfrac{Distance}{number/Volume} \\\\\\\sf\dashrightarrow \red{ D = \dfrac{Volume*Distance}{Area*time}}$

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$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Using Dimensional Formula :- }}}}$

$\sf\dashrightarrow D= \dfrac{ [L^3]\times [L]}{[L^2]\times [T]} \\\\\\\sf\dashrightarrow \boxed{\pink{\sf D= [M^0 L^2T^{-1}] }}$

Hence the Dimensional Formula is [M⁰L²T-¹] .