Integer type answer?

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Answer 1 · 2018-05-09T09:03:21

Let #r# be radius of divided drop. Equating volume of liquids in both cases we get

#4/3piR^3=K(4/3pir^3)#
#=>r^3=R^3/K#
#=>r=R/root3 (K)# .....(1)

We know that surface energy #E# and surface tension #T# are related by the expression

#dE = T (dA)# .....(2)
where #dA# is the change in surface area

Now change in surface area #dA=K(4pir^2)-4piR^2#
Using (1) above can be written as

#dA=K4pi(R/root3 (K))^2-4piR^2#
#dA=4piR^2(root3K-1)# .......(3)

Inserting various values in (2) we get

#10^-3 = 0.1/(4pi)(4pi(10^-2)^2(root3K-1))#
# => (root3K-1)=100#
# => root3K=101#
# => K=(101)^3# ......(4)

Given #K=10^alpha#. Taking #log_10# of both sides

#alpha=log_10 K#

Using (4)

#alpha=log_10(101)^3#
#=>alpha=6.01#, two decimal places