In a Sorvall T-865 fixed-angle rotor, the distance to the axis of rotation is 3.84 cm at the top of the tube and 9.10 cm at the bottom of the tube. Calculate the RCF at 20,000 rpm at the top and the bottom of the tube.
The Correct Answer and Explanation is:
To calculate the relative centrifugal force (RCF) at different positions in a centrifuge tube, we use the formula:RCF=1.118×10−5×r×(RPM)2\text{RCF} = 1.118 \times 10^{-5} \times r \times (\text{RPM})^2RCF=1.118×10−5×r×(RPM)2
Where:
- RCF\text{RCF}RCF is in units of g (gravitational force),
- rrr is the radius or distance from the axis of rotation (in cm),
- RPM\text{RPM}RPM is the rotational speed (in revolutions per minute).
Given:
- RPM = 20,000
- rtop=3.84 cmr_{\text{top}} = 3.84 \, \text{cm}rtop=3.84cm
- rbottom=9.10 cmr_{\text{bottom}} = 9.10 \, \text{cm}rbottom=9.10cm
Step 1: Calculate RCF at the top of the tube
RCFtop=1.118×10−5×3.84×(20000)2\text{RCF}_{\text{top}} = 1.118 \times 10^{-5} \times 3.84 \times (20000)^2RCFtop=1.118×10−5×3.84×(20000)2RCFtop=1.118×10−5×3.84×400,000,000\text{RCF}_{\text{top}} = 1.118 \times 10^{-5} \times 3.84 \times 400,000,000RCFtop=1.118×10−5×3.84×400,000,000RCFtop≈1.118×3.84×4000≈17151.55 g\text{RCF}_{\text{top}} \approx 1.118 \times 3.84 \times 4000 \approx 17151.55 \, gRCFtop≈1.118×3.84×4000≈17151.55g
Step 2: Calculate RCF at the bottom of the tube
RCFbottom=1.118×10−5×9.10×(20000)2\text{RCF}_{\text{bottom}} = 1.118 \times 10^{-5} \times 9.10 \times (20000)^2RCFbottom=1.118×10−5×9.10×(20000)2RCFbottom=1.118×10−5×9.10×400,000,000\text{RCF}_{\text{bottom}} = 1.118 \times 10^{-5} \times 9.10 \times 400,000,000RCFbottom=1.118×10−5×9.10×400,000,000RCFbottom≈1.118×9.10×4000≈40788.88 g\text{RCF}_{\text{bottom}} \approx 1.118 \times 9.10 \times 4000 \approx 40788.88 \, gRCFbottom≈1.118×9.10×4000≈40788.88g
Final Answers:
- RCF at the top of the tube ≈ 17,152 g
- RCF at the bottom of the tube ≈ 40,789 g
Explanation
In centrifugation, Relative Centrifugal Force (RCF) is the force exerted on particles during spinning, expressed as a multiple of Earth’s gravitational force (g). It’s a critical factor for efficient separation of components in biological or chemical samples. RCF depends on both the rotational speed (RPM) and the distance from the axis of rotation (radius, r). The farther a sample is from the center, the greater the force it experiences.
This calculation uses a Sorvall T-865 fixed-angle rotor, where the tubes are held at an angle, so different parts of the sample sit at different radii. In this case, the sample spans from 3.84 cm (top) to 9.10 cm (bottom) from the axis. When spinning at 20,000 rpm, particles at the bottom of the tube experience significantly more force than those at the top because RCF is directly proportional to the radius.
This difference in RCF within a single tube explains why particles sediment toward the bottom during centrifugation. It also highlights the importance of specifying RCF instead of RPM in protocols, because the same RPM produces different forces in different rotors or even different positions within a rotor.
The calculations show that RCF increases from about 17,152 g at the top to 40,789 g at the bottom of the tube. This range is crucial for separating particles based on density and size. For precise lab work, particularly in molecular biology or clinical diagnostics, knowing the exact RCF ensures reproducibility and efficiency of separations.
Hence, understanding and calculating RCF at different positions within a centrifuge tube is essential for correct interpretation and application of centrifugation results.
