酵母菌计数问题

问题

10ml培养基中有N个酵母菌，稀释100倍后采用16x25血细胞计数板计数，若某时刻中格细胞平均数量为25，求N的值

思考

Considering various methodologies

I’m having a look at the question's context, determining whether it involves 9 large or 25 smaller squares for counting yeast cells in dilution. The average count of 25 cells from 9 large squares is the current focus.

Piecing together

I’m working through the standard hemocytometer counting method, using a 16x25 configuration and considering the depth measurement of 0.1 mm. This involves calculating cell concentration and dilution factors.

Determining cell concentration

I’m thinking through the average cell count in a hemocytometer's small squares to find the initial yeast cell concentration. The arrangement involves central squares subdivided into smaller squares.

Figuring out the volume

OK, let me see—each small square in the hemocytometer has a volume of 2.5e-7 ml. This setup involves subdividing large squares into 16 smaller ones, each with a specific volume measurement.

Understanding the setup

I'm mapping out the cell concentration in the hemocytometer based on the average count in the small squares. The "16x25" configuration likely refers to the central rectangular counting area.

Figuring out the counting area

Mapping out whether "中格" refers to the entire 1 mm^2 central area or the smaller subdivisions in a hemocytometer. This gives clarity on the precise counting region.

Calculating initial concentration

I’m working through the cell concentration in the diluted sample, finding 25 cells in a 1 mm^2 area with 0.1 mm depth, leading to an initial concentration of 2.5 * 10^7 cells/ml.

Estimating cell count

Starting with an original sample concentration of 2.5 * 10^7 cells/ml, I’m calculating the total cell number in a 10 ml volume, considering the RBC counting method and average count ambiguity.

Calculating average and volume

I’m trying to determine if the average count of 25 cells refers to one large square, with a total area of 1 mm^2 subdivided into 25 small squares, each 0.04 mm^2 in area.

Calculating cell density

I converted the volume of the square to milliliters and determined that an average count of 25 cells in the large square corresponds to a concentration of 6.25e6 cells/ml.

Confirming RBC counting volume

OK, let's break down the central area for RBC counting. Each large square measures 4e-6 ml, crucial for accurate concentration arithmetic.

Calculating the final count

I’m working through the total cell count in a 10 ml sample, starting with a 6.25e6 cells/ml concentration in the diluted sample, then adjusting for the 100-fold dilution.

Confirming RBC counting

I’m verifying the RBC counting method, noting that an average count of 25 cells in a 1 mm^2 region translates to a concentration of 2.5e5 cells/ml in the diluted sample.

Evaluating ambiguity

Noticing two distinct results based on the ambiguity of "中格." RBC counting typically involves five squares in the central region, with each large square measuring 0.04 mm^2.

Taking a closer look

I’m noting that RBC counting involves averaging counts in five medium squares, with a total area of 0.2 mm^2, to determine the concentration per ml.

Working through RBC volume

I’m clarifying the volume of an RBC square, ensuring consistency with a depth of 0.1 mm and an area of 0.04 mm^2, which totals 4e-3 mm^3.

Calculating volume and concentration

I’m figuring out the RBC concentration by measuring the volume of the center square, divided into 25 RBC squares, and converting the count in one RBC square to cells/ml in the diluted sample.

Verifying the counting method

OK, let me see. Then, I'll ensure the 6.25e9 cells/ml result aligns with the expected RBC method, focusing on the central large square with 25 medium squares for yeast.

Revisiting the method

I'm considering the standard RBC counting method, focusing on the central large square subdivided into 25 smaller squares, to ensure the counting approach aligns with the expected results.

Confirming the volume

I’m mapping the volume of the center square (1 mm^2) in the hemocytometer, which yields a concentration of 2.5e7 cells/ml for the original sample after factoring in the dilution.

Thought about yeast cell counting，持续 53 秒

回答

要弄清这道题，关键在于辨明“中格”所代表的计数区域以及该区域对应的体积。常见的（改良）Neubauer 计数板通常分为：

九大方格(3×3)，每个大方格面积 1 mm^2，深度 0.1 mm。
中央大方格(即中格) 再细分为 25 个中方格（每个中方格面积 0.04 mm^2，深度同为 0.1 mm），用于红细胞或微生物计数；进一步每个中方格里又细分为 16 个小方格，用于更细的计数需求。

题目里提到“16×25 血细胞计数板”通常就是指这种改良 Neubauer，中央那块 1 mm^2 的区域被分成 25 个中方格，每个中方格再有 16 个小格。不过在中文习惯里，“中格”往往指的是中央 1 mm^2 的那整块(而不是再往里细分到每个 0.04 mm^2 的中方格或者 0.0025 mm^2 的小格)。题目给出的信息也通常是按照“中央大方格 = 1 mm^2”这一整块来处理。

1. 明确计数区域及其体积

如果“中格”指的是整个中央 1 mm^2 区域，则它的面积为 1 mm^2，计数板盖玻片与计数室之间的深度为 0.1 mm。
- 该区域对应的体积 = 面积 × 深度 = 1 mm^2 × 0.1 mm = 0.1 mm^3
- 1 mm^3 = 0.001 mL，所以 0.1 mm^3 = 0.0001 mL = 1×10^-^4 mL

由此，若在“整个中央大方格”里数到 25 个细胞，那么在该稀释后的液体里，其细胞浓度为：

\text{(稀释液中细胞浓度, 个/mL)} = \frac{\text{计数板中细胞数}}{\text{该区域体积 (mL)}} = \frac{25}{1 \times 10^{-4}} = 2.5 \times 10^5 \,(\text{个/mL})

2. 考虑稀释倍数

题中说“稀释 100 倍后”进行计数，因此原液(未稀释前)的浓度要再乘以 100 倍：

\text{原液浓度} = 2.5\times 10^5 \times 100 = 2.5 \times 10^7 \,(\text{个/mL})

3. 计算培养基中的总细胞数 $N$

题目给的是总培养基体积为 10 mL，那么原液里(即未稀释状态下)总的酵母菌数 $N$ 为：

N = (\text{原液浓度, 个/mL}) \times (\text{总容量, mL}) = 2.5 \times 10^7 \,\text{个/mL} \times 10 \,\text{mL} = 2.5 \times 10^8 \,\text{个}

4. 答案

\boxed{N = 2.5 \times 10^8}

进一步说明（为何不是按“25 个中方格”或“16 小格”来算？）

若题目明确说“在一个中方格（面积 0.04 mm^2）里数到 25 个”，那么体积只剩下 0.04 mm^2 × 0.1 mm = 0.004 mm^3 = 4×10^-^6 mL，对应的浓度会大大提高。
但是绝大多数教科书/习惯用法里，“中格”都指 1 mm^2 的那整个中心大方格区域，这也是本题最常见、最合理的解释。

因此，按照常规理解，本题正确做法便是把中心 1 mm^2 整块视为计数区域，总体积 1×10^-^4 mL，数到 25 个菌，结算得到 $2.5\times 10^8$ 个酵母菌。

问题

思考

回答

1. 明确计数区域及其体积

2. 考虑稀释倍数

3. 计算培养基中的总细胞数 NNN

4. 答案

进一步说明（为何不是按“25 个中方格”或“16 小格”来算？）

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3. 计算培养基中的总细胞数 $N$