Q-
According to bohr's atomic theory for an electron in its nth orbit:
mvr = nh2Î
suppose the velocity of an electron(m= 9.109*10-31) revolving in an orbit of radius 'r' is found to be v=1.4504*106 ,then:
(i)find no of significant figures in 'r'
(ii)find value of x+y+z ,where
x= no of significant figures in 'r'
y= no of significant figures in 'v'
z = no of significant figures in the digit 2 in the term nh2Î
1plz verify me..z should be ∞ shouldnt it?
its a numeric constant in the expression n we know its exact value..
about (i),dont u think the number of significant figures in h wil b necessary?r will hav the same number of significant numbers as the one containinig the least nunmber of sig figures in the division.
1the same thing i wanted to ask in (i):
while comparing which term(in nh2Î ) has least significant figures ,would the significant figures of 'n' and 'h' would also be important
(my main question is that,while finding significant figures in one term of a formula(like 'r' in above question), do we also compare significant figures of physical constants in a formula ?)
your answer to (ii) is right
one more question:
i agree that the 2 in (ii) has ∞ significant figures as it is a exact value
now the n in nh2Î is also an exact number but we don't universally know its exact value (i mean it has to calculated) (and sometimes it is calculated experimently also.So would we compare the significant figures of 'n' while calculating significant figures of 'r'in (i) because in that case the answer to (i) will directly be =1(as no. of significant figures of 'n' is least of all ie 1)
1pritish,n also will have an exact value..so even it would have infinite number of significant figures..in the sense that its value is known exactly and thus it does affect the correctness of the calculation.we know that n has to be a natural number.
the problem will be with h.say if one takes it as 6.626*10-34,and someone as 6.626068×10-34,the number of significant figures will be different..
1generally speaking that value of 'h' must be taken which has most significant figures because it will give the most accurate value of 'r'
but if it asked as a question the value of 'h' will surely be given in the question we will compare it's significant figures according to that given value only
the main problem is of 'n' .I know it is an exact +ve integer value but it is so, because we have to assume it to be like that only.While doing any question of ATOMIC STRUCTURE regarding calculation of 'n' we never find 'n' as an integer.normally we find it as 3.001 or 4.023etcand we round off them to 3 and 4 respectively and we know that rounded off no's can't be assumed as having ∞ significant figures (like 2 in nh2Π) so i think 'n' would have 1 significant figure only but thats only my opinion
1so we're having a confusion over n,isnt it..
but c pritish,as i said n has to be a natural number..
here's a nice note i found on chemistry.about.com:
"Exact Numbers
Sometimes numbers used in a calculation are exact rather than approximate. This is true when using defined quantities, including many conversion factors, and when using pure numbers. Pure or defined numbers do not affect the accuracy of a calculation. You may think of them as having an infinite number of significant figures. Pure numbers are easy to spot because they have no units. Defined values or conversion factors, like measured values, may have units. Practice identifying them!
Example:
You want to calculate the average height of three plants and measure the following heights: 30.1 cm, 25.2 cm, 31.3 cm; with an average height of (30.1 + 25.2 + 31.3)/3 = 86.6/3 = 28.87 = 28.9 cm. There are three significant figures in the heights. Even though you are dividing the sum by a single digit, the three significant figures should be retained in the calculation."
we're multiplying the expression by n which will have an exact value,so i think it should not be 1 sig figure only in the result..