Answer the question which is given in attachment.
Answers
is the Number of particles per unit Area per unit Time.
Now, number of particles can be taken as unitless, or we can give the name "mole", which after all has no dimensions.
So, Dimension would be:
and are Number of particles per unit volume
Their dimensions would be:
and are positions at Z-axis. They simply have the unit metre and have the dimension of [ L ] .
Now, we can find the dimensions of D.
Thus, the answer is Option (3).
Hope it helps
Purva
Brainly Community
Here we first need to understand what each term means:
NN is the Number of particles per unit Area per unit Time.
Now, number of particles can be taken as unitless, or we can give the name "mole", which after all has no dimensions.
So, Dimension would be:
\begin{lgathered}[ \, N \, ] = \frac{1}{[ \, Area \, \times \, Time\, ]} \\ \\ \\ \implies [ \, N \, ] = \frac{1}{[ \, L^2 \, ] \, \, [\, T \, ] } \\ \\ \\ \implies [ \, N \, ] = [ \, L^{-2} \, T^{-1} \, ]\end{lgathered}
[N]=
[Area×Time]
1
⟹[N]=
[L
2
][T]
1
⟹[N]=[L
−2
T
−1
]
N_1N
1
and N_2N
2
are Number of particles per unit volume
Their dimensions would be:
\begin{lgathered}[\, N_1 \, ] = \frac{1}{[\, Volume \, ]} \\ \\ \\ \implies [ \, N_1 \, ] = \frac{1}{[ \, L^3 \, ]} \\ \\ \\ \implies [ \, N_1 \, ] = [ \, N_2 \, ] = [ \, L^{-3} \, ]\end{lgathered}
[N
1
]=
[Volume]
1
⟹[N
1
]=
[L
3
]
1
⟹[N
1
]=[N
2
]=[L
−3
]
Z_1Z
1
and Z_2Z
2
are positions at Z-axis. They simply have the unit metre and have the dimension of [ L ] .
Now, we can find the dimensions of D.
\begin{lgathered}N = -D \frac{(N_2-N_1)}{(Z_2-Z_1)} \\ \\ \\ \implies [ \, N \, ] = [ \, D \, ] \, \frac{[\, N_1 \, ]}{[ \, Z_1 \, ]} \\ \\ \\ \implies [ \, L^{-2} \, T^{-1} \, ] = [ \, D \, ] \, \frac{[ \, L^{-3} \, ]}{[\, L \, ]} \\ \\ \\ \implies [\, L^{-2} \, T^{-1} \, ] = [ \, D \, ] \, \, [\, L^{-4} \, ] \\ \\ \\ \implies [ \, D \, ] = \frac{[\, L^{-2} \, T^{-1} \, ]}{[ \, L^{-4} \, ]} \\ \\ \\ \\ \implies \boxed{[ \, D \, ] = [ \, L^2 \, T^{-1} \, ]} \\ \\ \\ \\ \implies \boxed{[ \, D \, ] = [ \, M^0 \, L^2 \, T^{-1} \, ]}\end{lgathered}
N=−D
(Z
2
−Z
1
)
(N
2
−N
1
)
⟹[N]=[D]
[Z
1
]
[N
1
]
⟹[L
−2
T
−1
]=[D]
[L]
[L
−3
]
⟹[L
−2
T
−1
]=[D][L
−4
]
⟹[D]=
[L
−4
]
[L
−2
T
−1
]
⟹
[D]=[L
2
T
−1
]
⟹
[D]=[M
0
L
2
T
−1
]
Thus, the answer is Option (3).
N1 and N2 are number of particles per unit volume
Z1 and Z2 are positions at Z-axis. [Their unit is metre]
Now try the question