The shape Of Tobacco Mosaic Virus (TMC) is cylindrical, having length and diameter 3000 A and 170 A, respectively. The density of the virus is 0.08 gm/ml. The molecular weight of TMC ‚Äãis
(A) 3.28 (B) 5.44 x 10-24
(C) 5.44 x 10-18 (D) 3.28 106
Answers
answer : option (D)
explanation : length and diameter of TMC virus are 3000A° and 170A° respectively.
i.e., l = 3000A° = 3 × 10^-7 m
d = 170A° , r = d/2 = 85A° = 8.5 × 10^-9m
now, volume of cylindrical TMC virus , V = πr²l
= 3.14 × (8.5 × 10^-9)² × 3 × 10^-7 m³
= 680.595 × 10^-25 m³
= 6.80595 × 10^-23 m³
The density of virus is given, d = 0.08g/cm³ = 0.08 × 10³ kg/m³
= 80 kg/m³
now, mass of virus = density × volume
= 80 × 6.80595 × 10^-23 kg
= 544.476 × 10^-23 kg
= 5.44476 × 10^-21 kg
≈ 5.44 × 10^-21 kg
now molecular weight of TMC virus = mass of one molecule of TMC virus × Avogadro's number
= 5.44 × 10^-21 × 6.023 × 10²³ kg
= 32.8 × 10² kg
= 3.28 × 10^6 g
hence, molecular weight of TMC virus is 3.28 × 10^6 g/mol
Option (D)
Explanation:
The diameter and length of TMC virus are 3000A° and 170A° respectively.
i.e., l = 3000A° = 3 × 10^-7 m
d = 170A° , r = d/2 = 85A° = 8.5 × 10^-9m
V = πr²l
= 3.14 × (8.5 × 10^-9)² × 3 × 10^-7 m³
= 680.595 × 10^-25 m³
= 6.80595 × 10^-23 m³
The virus’s density is given as, d = 0.08g/cm³ = 0.08 × 10³ kg/m³
= 80 kg/m³
Mass of virus = density × volume
= 80 × 6.80595 × 10^-23 kg
= 544.476 × 10^-23 kg
= 5.44476 × 10^-21 kg
≈ 5.44 × 10^-21 kg
Molecular weight of TMC virus = mass of one molecule of TMC virus × Avogadro's number
= 5.44 × 10^-21 × 6.023 × 10²³ kg
= 32.8 × 10² kg
= 3.28 × 10^6 g
So, molecular weight of TMC virus is 3.28 × 10^6 g/mol .
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