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P = P°e^-αt ²
where p° is constant.
concept :- exponential functions are dimentionless quantities,
it means e^- αt² is a dimentionless quantitiy .
so, -αt² is also a dimentionless quantity ,
but we know time is dimentional.quantity
, dimension of time = [ T ]
so, αt² is a dimensionless only if
dimension of α = 1/dimension of t²
but we know dimension of t² =[ T² ]
hence,
dimension of α = 1/[ T²] = [ T^-2 ]
hence option (2) is correct answer
where p° is constant.
concept :- exponential functions are dimentionless quantities,
it means e^- αt² is a dimentionless quantitiy .
so, -αt² is also a dimentionless quantity ,
but we know time is dimentional.quantity
, dimension of time = [ T ]
so, αt² is a dimensionless only if
dimension of α = 1/dimension of t²
but we know dimension of t² =[ T² ]
hence,
dimension of α = 1/[ T²] = [ T^-2 ]
hence option (2) is correct answer
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