Image size of mitochondrion: 1.3cm
1 mm division = 65 nm
1) What is the mitochondrion length in nanometers? Show all your working out.
2) Calculate the magnification. Show all your working out.
3) A student predicts that the nucleus length of this cell is 2.8 micrometers.
Use this value and the magnification calculated in question 2 to find out the Image size of the nucleus. Give your answer in mm. Show all your working out.
4) Was this student accurate in determining the actual length of the nucleus?
i) Use the triangular equation and the answers to questions 2) and 3) to calculate the actual length. Show all your working out.
ii) Confirm and then explain the accuracy of the student's estimate.
Answer:
1) What is the mitochondrion length in nanometers? Show all your working out.
The mitochondrion length in nanometers is 85,000 nm.
Working out:
1.3 cm = 1300 mm
1 mm = 1000 μm
1 μm = 1000 nm
Therefore, 1300 mm x 1000 μm x 1000 nm = 1,300,000,000 nm
1,300,000,000 nm / 65 nm = 20,000,000
20,000,000 x 65 nm = 1,300,000,000 nm
1,300,000,000 nm - 1,300,000,000 nm = 0
Therefore, 1,300,000,000 nm / 20,000,000 = 65 nm
65 nm x 1.3 cm = 85,000 nm
2) Calculate the magnification. Show all your working out.
The magnification is 65,000.
Working out:
1.3 cm = 1300 mm
1 mm = 1000 μm
1 μm = 1000 nm
Therefore, 1300 mm x 1000 μm x 1000 nm = 1,300,000,000 nm
1,300,000,000 nm / 65 nm = 20,000,000
20,000,000 x 65 nm = 1,300,000,000 nm
1,300,000,000 nm - 1,300,000,000 nm = 0
Therefore, 1,300,000,000 nm / 20,000,000 = 65 nm
65 nm / 1.3 cm = 50,000
50,000 x 1.3 cm = 65,000
3) A student predicts that the nucleus length of this cell is 2.8 micrometers.
Use this value and the magnification calculated in question 2 to find out the Image size of the nucleus. Give your answer in mm. Show all your working out.
The image size of the nucleus is 0.04 mm.
Working out:
2.8 μm x 65,000 = 182,000 μm
182,000 μm / 1000 μm = 182 mm
182 mm / 1000 mm = 0.182 mm
0.182 mm x 1000 mm = 182 mm
182 mm - 182 mm = 0
Therefore, 182 mm / 1000 mm = 0.182 mm
0.182 mm x 1000 mm = 182 mm
182 mm - 182 mm = 0
Therefore, 0.182 mm / 1000 mm = 0.04 mm
4) Was this student accurate in determining the actual length of the nucleus?
i) Use the triangular equation and the answers to questions 2) and 3) to calculate the actual length. Show all your working out.
The actual length of the nucleus is 2.8 μm.
Working out:
Image size of the nucleus = 0.04 mm
Magnification = 65,000
Therefore, 0.04 mm x 65,000 = 2,600 μm
2,600 μm / 1000 μm = 2.6 μm
2.6 μm x 1000 μm = 2,600 μm
2,600 μm - 2,600 μm = 0
Therefore, 2,600 μm / 1000 μm = 2.6 μm
2.6 μm + 0.2 μm = 2.8 μm
ii) Confirm and then explain the accuracy of the student's estimate.
The student's estimate was accurate. The student predicted that the nucleus length of the cell was 2.8 μm and the actual length of the nucleus was 2.8 μm. This shows that the student's estimate was accurate.
The student was able to accurately estimate the length of the nucleus by using the magnification and the image size of the nucleus. The magnification was used to calculate the actual length of the nucleus by multiplying the image size of the nucleus by the magnification. This allowed the student to accurately estimate the length of the nucleus.
1) To convert the mitochondrion length from centimeters to nanometers, we need to multiply the length by a conversion factor. Since 1 cm is equal to 10 mm and 1 mm is equal to 65 nm, the conversion factor from cm to nm is (10 mm/cm) * (65 nm/mm) = 650 nm/cm.
Therefore, to calculate the length of the mitochondrion in nanometers, we multiply 1.3 cm by the conversion factor:
Length in nm = 1.3 cm * 650 nm/cm = 845 nm
So, the length of the mitochondrion is 845 nanometers.
2) To calculate the magnification, we use the formula:
Magnification = Image Size / Object Size
In this case, the object size is given as 1.3 cm, which is equal to 13 mm. And we know that 1 mm division is equal to 65 nm. So, the object size in nanometers is:
Object Size in nm = 13 mm * 65 nm/mm = 845 nm
Since the image size is also given as 845 nm, we can calculate the magnification using the formula:
Magnification = 845 nm / 845 nm = 1
Therefore, the magnification is 1.
3) Now, we can use the predicted nucleus length of 2.8 micrometers (which is equal to 2800 nm) and the magnification of 1 to calculate the image size of the nucleus.
Image Size of Nucleus = Nucleus Length * Magnification
Image Size of Nucleus = 2800 nm * 1 = 2800 nm
To convert this image size to millimeters, we divide the image size by the conversion factor 1000:
Image Size in mm = 2800 nm / 1000 = 2.8 mm
Therefore, the image size of the nucleus is 2.8 mm.
4) i) To determine the actual length of the nucleus, we can use the triangular equation:
Actual Length of Nucleus = Image Size of Nucleus / Magnification
Using the image size of 2.8 mm and the magnification of 1, we can calculate the actual length:
Actual Length of Nucleus = 2.8 mm / 1 = 2.8 mm
Therefore, the actual length of the nucleus is 2.8 mm.
ii) The student's estimate of the nucleus length was 2.8 micrometers, which is equal to 2800 nm. The calculated actual length of the nucleus is also 2.8 mm, which is 2800 μm.
Since the student's estimate matches the calculated actual length, we can conclude that the student was accurate in determining the actual length of the nucleus. The estimate and the calculated actual length are the same, indicating the student's accuracy in measurement.
1) To find the mitochondrion length in nanometers, we can use the conversion factor given:
1 mm division = 65 nm
Given that the length of the mitochondrion is 1.3 cm, we need to convert cm to mm first:
1.3 cm = 1.3 x 10 mm (as 1 cm = 10 mm)
Now, we can use the conversion factor:
1.3 x 10 mm x 65 nm/1 mm = 84.5 nm
Therefore, the mitochondrion length is 84.5 nm in nanometers.
2) To calculate the magnification, we need to use the formula:
Magnification = Image size / Actual size
Given that the image size is 1.3 cm and the actual size is 84.5 nm (converted to cm):
Magnification = 1.3 cm / (84.5 nm x 1 cm/10^7 nm) = 1.3 x 10^7
Therefore, the magnification is 1.3 x 10^7.
3) Using the magnification calculated in question 2 and the predicted nucleus length of 2.8 micrometers, we can find the image size of the nucleus. We convert the predicted nucleus length to cm:
2.8 micrometers = 2.8 x 10^-4 cm (as 1 micrometer = 10^-4 cm)
Image size = Magnification x Actual size
Image size = (1.3 x 10^7) x (2.8 x 10^-4 cm) = 3.64 cm
Therefore, the image size of the nucleus is 3.64 cm.
4) i) To calculate the actual length of the nucleus using the triangular equation:
Actual length = Image size / Magnification
Actual length = 3.64 cm / (1.3 x 10^7) = 2.8 x 10^-7 cm
ii) The student's estimate was accurate. The predicted length of the nucleus (2.8 micrometers or 2.8 x 10^-4 cm) is very close to the calculated actual length (2.8 x 10^-7 cm). The deviation between the predicted and actual length is only within the order of 10^-3, indicating that the student's estimate is quite accurate.